diff --git a/apps/emqx_bridge/test/emqx_bridge_api_SUITE.erl b/apps/emqx_bridge/test/emqx_bridge_api_SUITE.erl
index 6b160f3b3..fdbbc5376 100644
--- a/apps/emqx_bridge/test/emqx_bridge_api_SUITE.erl
+++ b/apps/emqx_bridge/test/emqx_bridge_api_SUITE.erl
@@ -1154,7 +1154,7 @@ t_bridges_probe(Config) ->
     ?assertMatch(
         {ok, 400, #{
             <<"code">> := <<"TEST_FAILED">>,
-            <<"message">> := <<"Connection refused">>
+            <<"message">> := <<"Connection refused", _/binary>>
         }},
         request_json(
             post,
diff --git a/apps/emqx_bridge_mqtt/src/emqx_bridge_mqtt_connector.erl b/apps/emqx_bridge_mqtt/src/emqx_bridge_mqtt_connector.erl
index 118542356..6b9a40123 100644
--- a/apps/emqx_bridge_mqtt/src/emqx_bridge_mqtt_connector.erl
+++ b/apps/emqx_bridge_mqtt/src/emqx_bridge_mqtt_connector.erl
@@ -98,7 +98,7 @@ on_start(ResourceId, #{server := Server} = Conf) ->
                 server => Server
             }};
         {error, Reason} ->
-            {error, Reason}
+            {error, emqx_maybe:define(explain_error(Reason), Reason)}
     end.
 
 on_add_channel(
@@ -200,7 +200,7 @@ on_get_channel_status(
     } = _State
 ) when is_map_key(ChannelId, Channels) ->
     %% The channel should be ok as long as the MQTT client is ok
-    connected.
+    ?status_connected.
 
 on_get_channels(ResId) ->
     emqx_bridge_v2:get_channels_for_connector(ResId).
@@ -356,10 +356,15 @@ on_get_status(_ResourceId, State) ->
     Workers = [{Pool, Worker} || {Pool, PN} <- Pools, {_Name, Worker} <- ecpool:workers(PN)],
     try emqx_utils:pmap(fun get_status/1, Workers, ?HEALTH_CHECK_TIMEOUT) of
         Statuses ->
-            combine_status(Statuses)
+            case combine_status(Statuses) of
+                {Status, Msg} ->
+                    {Status, State, Msg};
+                Status ->
+                    Status
+            end
     catch
         exit:timeout ->
-            connecting
+            ?status_connecting
     end.
 
 get_status({_Pool, Worker}) ->
@@ -367,7 +372,7 @@ get_status({_Pool, Worker}) ->
         {ok, Client} ->
             emqx_bridge_mqtt_ingress:status(Client);
         {error, _} ->
-            disconnected
+            ?status_disconnected
     end.
 
 combine_status(Statuses) ->
@@ -375,11 +380,25 @@ combine_status(Statuses) ->
     %% Natural order of statuses: [connected, connecting, disconnected]
     %% * `disconnected` wins over any other status
     %% * `connecting` wins over `connected`
-    case lists:reverse(lists:usort(Statuses)) of
+    ToStatus = fun
+        ({S, _Reason}) -> S;
+        (S) when is_atom(S) -> S
+    end,
+    CompareFn = fun(S1A, S2A) ->
+        S1 = ToStatus(S1A),
+        S2 = ToStatus(S2A),
+        S1 > S2
+    end,
+    case lists:usort(CompareFn, Statuses) of
+        [{Status, Reason} | _] ->
+            case explain_error(Reason) of
+                undefined -> Status;
+                Msg -> {Status, Msg}
+            end;
         [Status | _] ->
             Status;
         [] ->
-            disconnected
+            ?status_disconnected
     end.
 
 mk_ingress_config(
@@ -514,15 +533,54 @@ connect(Pid, Name) ->
             {ok, Pid};
         {error, Reason} = Error ->
             IsDryRun = emqx_resource:is_dry_run(Name),
-            ?SLOG(?LOG_LEVEL(IsDryRun), #{
-                msg => "ingress_client_connect_failed",
-                reason => Reason,
-                resource_id => Name
-            }),
+            log_connect_error_reason(?LOG_LEVEL(IsDryRun), Reason, Name),
             _ = catch emqtt:stop(Pid),
             Error
     end.
 
+log_connect_error_reason(Level, {tcp_closed, _} = Reason, Name) ->
+    ?tp(emqx_bridge_mqtt_connector_tcp_closed, #{}),
+    ?SLOG(Level, #{
+        msg => "ingress_client_connect_failed",
+        reason => Reason,
+        name => Name,
+        explain => explain_error(Reason)
+    });
+log_connect_error_reason(Level, econnrefused = Reason, Name) ->
+    ?tp(emqx_bridge_mqtt_connector_econnrefused_error, #{}),
+    ?SLOG(Level, #{
+        msg => "ingress_client_connect_failed",
+        reason => Reason,
+        name => Name,
+        explain => explain_error(Reason)
+    });
+log_connect_error_reason(Level, Reason, Name) ->
+    ?SLOG(Level, #{
+        msg => "ingress_client_connect_failed",
+        reason => Reason,
+        name => Name
+    }).
+
+explain_error(econnrefused) ->
+    <<
+        "Connection refused. "
+        "This error indicates that your connection attempt to the MQTT server was rejected. "
+        "In simpler terms, the server you tried to connect to refused your request. "
+        "There can be multiple reasons for this. "
+        "For example, the MQTT server you're trying to connect to might be down or not "
+        "running at all or you might have provided the wrong address "
+        "or port number for the server."
+    >>;
+explain_error({tcp_closed, _}) ->
+    <<
+        "Your MQTT connection attempt was unsuccessful. "
+        "It might be at its maximum capacity for handling new connections. "
+        "To diagnose the issue further, you can check the server logs for "
+        "any specific messages related to the unavailability or connection limits."
+    >>;
+explain_error(_Reason) ->
+    undefined.
+
 handle_disconnect(_Reason) ->
     ok.
 
diff --git a/apps/emqx_bridge_mqtt/src/emqx_bridge_mqtt_ingress.erl b/apps/emqx_bridge_mqtt/src/emqx_bridge_mqtt_ingress.erl
index 1749d4194..35aea67a6 100644
--- a/apps/emqx_bridge_mqtt/src/emqx_bridge_mqtt_ingress.erl
+++ b/apps/emqx_bridge_mqtt/src/emqx_bridge_mqtt_ingress.erl
@@ -19,6 +19,7 @@
 -include_lib("emqx/include/logger.hrl").
 -include_lib("emqx/include/emqx_mqtt.hrl").
 -include_lib("snabbkaffe/include/snabbkaffe.hrl").
+-include_lib("emqx_resource/include/emqx_resource.hrl").
 
 %% management APIs
 -export([
@@ -234,13 +235,13 @@ status(Pid) ->
     try
         case proplists:get_value(socket, info(Pid)) of
             Socket when Socket /= undefined ->
-                connected;
+                ?status_connected;
             undefined ->
-                connecting
+                ?status_connecting
         end
     catch
         exit:{noproc, _} ->
-            disconnected
+            ?status_disconnected
     end.
 
 %%
diff --git a/apps/emqx_bridge_mqtt/test/emqx_bridge_mqtt_SUITE.erl b/apps/emqx_bridge_mqtt/test/emqx_bridge_mqtt_SUITE.erl
index a220eb9f7..42cf9d2b8 100644
--- a/apps/emqx_bridge_mqtt/test/emqx_bridge_mqtt_SUITE.erl
+++ b/apps/emqx_bridge_mqtt/test/emqx_bridge_mqtt_SUITE.erl
@@ -1025,31 +1025,39 @@ t_mqtt_conn_bridge_egress_async_reconnect(_) ->
     ct:sleep(1000),
 
     %% stop the listener 1883 to make the bridge disconnected
-    ok = emqx_listeners:stop_listener('tcp:default'),
-    ct:sleep(1500),
-    ?assertMatch(
-        #{<<"status">> := Status} when
-            Status == <<"connecting">> orelse Status == <<"disconnected">>,
-        request_bridge(BridgeIDEgress)
+    ?check_trace(
+        begin
+            ok = emqx_listeners:stop_listener('tcp:default'),
+            ct:sleep(1500),
+            ?assertMatch(
+                #{<<"status">> := Status} when
+                    Status == <<"connecting">> orelse Status == <<"disconnected">>,
+                request_bridge(BridgeIDEgress)
+            ),
+
+            %% start the listener 1883 to make the bridge reconnected
+            ok = emqx_listeners:start_listener('tcp:default'),
+            timer:sleep(1500),
+            ?assertMatch(
+                #{<<"status">> := <<"connected">>},
+                request_bridge(BridgeIDEgress)
+            ),
+
+            N = stop_publisher(Publisher),
+
+            %% all those messages should eventually be delivered
+            [
+                assert_mqtt_msg_received(RemoteTopic, Payload)
+             || I <- lists:seq(1, N),
+                Payload <- [integer_to_binary(I)]
+            ],
+            ok
+        end,
+        fun(Trace) ->
+            ?assertMatch([_ | _], ?of_kind(emqx_bridge_mqtt_connector_econnrefused_error, Trace)),
+            ok
+        end
     ),
-
-    %% start the listener 1883 to make the bridge reconnected
-    ok = emqx_listeners:start_listener('tcp:default'),
-    timer:sleep(1500),
-    ?assertMatch(
-        #{<<"status">> := <<"connected">>},
-        request_bridge(BridgeIDEgress)
-    ),
-
-    N = stop_publisher(Publisher),
-
-    %% all those messages should eventually be delivered
-    [
-        assert_mqtt_msg_received(RemoteTopic, Payload)
-     || I <- lists:seq(1, N),
-        Payload <- [integer_to_binary(I)]
-    ],
-
     ok.
 
 start_publisher(Topic, Interval, CtrlPid) ->
diff --git a/apps/emqx_bridge_mqtt/test/emqx_bridge_mqtt_v2_subscriber_SUITE.erl b/apps/emqx_bridge_mqtt/test/emqx_bridge_mqtt_v2_subscriber_SUITE.erl
index b9097b9c3..e0598fa1e 100644
--- a/apps/emqx_bridge_mqtt/test/emqx_bridge_mqtt_v2_subscriber_SUITE.erl
+++ b/apps/emqx_bridge_mqtt/test/emqx_bridge_mqtt_v2_subscriber_SUITE.erl
@@ -131,6 +131,9 @@ hookpoint(Config) ->
     BridgeId = bridge_id(Config),
     emqx_bridge_resource:bridge_hookpoint(BridgeId).
 
+simplify_result(Res) ->
+    emqx_bridge_v2_testlib:simplify_result(Res).
+
 %%------------------------------------------------------------------------------
 %% Testcases
 %%------------------------------------------------------------------------------
@@ -246,3 +249,46 @@ t_receive_via_rule(Config) ->
         end
     ),
     ok.
+
+t_connect_with_more_clients_than_the_broker_accepts(Config) ->
+    Name = ?config(connector_name, Config),
+    OrgConf = emqx_mgmt_listeners_conf:get_raw(tcp, default),
+    on_exit(fun() ->
+        emqx_mgmt_listeners_conf:update(tcp, default, OrgConf)
+    end),
+    NewConf = OrgConf#{<<"max_connections">> => 3},
+    {ok, _} = emqx_mgmt_listeners_conf:update(tcp, default, NewConf),
+    ?check_trace(
+        #{timetrap => 10_000},
+        begin
+            ?assertMatch(
+                {201, #{
+                    <<"status">> := <<"disconnected">>,
+                    <<"status_reason">> :=
+                        <<"Your MQTT connection attempt was unsuccessful", _/binary>>
+                }},
+                simplify_result(
+                    emqx_bridge_v2_testlib:create_connector_api(
+                        Config,
+                        #{<<"pool_size">> => 100}
+                    )
+                )
+            ),
+            ?block_until(#{?snk_kind := emqx_bridge_mqtt_connector_tcp_closed}),
+            ?assertMatch(
+                {200, #{
+                    <<"status">> := <<"disconnected">>,
+                    <<"status_reason">> :=
+                        <<"Your MQTT connection attempt was unsuccessful", _/binary>>
+                }},
+                simplify_result(emqx_bridge_v2_testlib:get_connector_api(mqtt, Name))
+            ),
+            ok
+        end,
+        fun(Trace) ->
+            ?assertMatch([_ | _], ?of_kind(emqx_bridge_mqtt_connector_tcp_closed, Trace)),
+            ok
+        end
+    ),
+
+    ok.
diff --git a/changes/ce/fix-13425.en.md b/changes/ce/fix-13425.en.md
new file mode 100644
index 000000000..e02e99c0a
--- /dev/null
+++ b/changes/ce/fix-13425.en.md
@@ -0,0 +1 @@
+The MQTT connector error log messages have been improved to provide clearer and more detailed information.