diff --git a/jupyter_server/gateway/connections.py b/jupyter_server/gateway/connections.py
index 37d62d2f7..2bce86be8 100644
--- a/jupyter_server/gateway/connections.py
+++ b/jupyter_server/gateway/connections.py
@@ -146,9 +146,10 @@ def handle_outgoing_message(self, incoming_msg: str, *args: Any) -> None:
     def handle_incoming_message(self, message: str) -> None:
         """Send message to gateway server."""
         if self.ws is None and self.ws_future is not None:
-            if self.ws_future.done() and isinstance(self.ws_future.exception(), Exception):
-                self.log.warning(f"Exception connect to websocket {self.ws_future.exception()}")
-                return
+            if self.ws_future.done() and self.ws_future.exception() is not None:
+                self.log.warning(
+                    "Ignoring message on failed connection to kernel %s", self.kernel_id
+                )
             loop = IOLoop.current()
             loop.add_future(self.ws_future, lambda future: self.handle_incoming_message(message))
         else: