diff --git a/src/textual_dev/client.py b/src/textual_dev/client.py
index bc9cd53..b1fd6e7 100644
--- a/src/textual_dev/client.py
+++ b/src/textual_dev/client.py
@@ -118,6 +118,8 @@ async def connect(self) -> None:
                 f"{self.url}/textual-devtools-websocket"
             )
         except (ClientConnectorError, ClientResponseError):
+            await self.session.close()
+            self.session = None
             raise DevtoolsConnectionError()
 
         log_queue = self.log_queue