diff --git a/tests/protocols/test_http.py b/tests/protocols/test_http.py
index 5c6c3e52a..60768346a 100644
--- a/tests/protocols/test_http.py
+++ b/tests/protocols/test_http.py
@@ -159,6 +159,18 @@
     b"".join([b"x" * 32 * 1024 + b"\r\n", b"\r\n", b"\r\n"]),
 ]
 
+UPGRADE_REQUEST_ERROR_FIELD = b"\r\n".join(
+    [
+        b"GET / HTTP/1.1",
+        b"Host: example.org",
+        b"Connection: upgrade",
+        b"Upgrade: not-websocket",
+        b"Sec-WebSocket-Version: 11",
+        b"",
+        b"",
+    ]
+)
+
 
 class MockTransport:
     def __init__(self, sockname=None, peername=None, sslcontext=False):
@@ -1080,3 +1092,35 @@ async def app(scope: Scope, receive: ASGIReceiveCallable, send: ASGISendCallable
         assert b"Hi!" in protocol.transport.buffer
 
     assert not expected_states  # consumed
+
+
+async def test_header_upgrade_is_not_websocket_depend_installed(
+    caplog: pytest.LogCaptureFixture, http_protocol_cls: HTTPProtocol
+):
+    caplog.set_level(logging.WARNING, logger="uvicorn.error")
+    app = Response("Hello, world", media_type="text/plain")
+
+    protocol = get_connected_protocol(app, http_protocol_cls)
+    protocol.data_received(UPGRADE_REQUEST_ERROR_FIELD)
+    await protocol.loop.run_one()
+    assert "Unsupported upgrade request." in caplog.text
+    msg = "No supported WebSocket library detected. Please use \"pip install 'uvicorn[standard]'\", or install 'websockets' or 'wsproto' manually."  # noqa: E501
+    assert msg not in caplog.text
+    assert b"HTTP/1.1 200 OK" in protocol.transport.buffer
+    assert b"Hello, world" in protocol.transport.buffer
+
+
+async def test_header_upgrade_is_websocket_depend_not_installed(
+    caplog: pytest.LogCaptureFixture, http_protocol_cls: HTTPProtocol
+):
+    caplog.set_level(logging.WARNING, logger="uvicorn.error")
+    app = Response("Hello, world", media_type="text/plain")
+
+    protocol = get_connected_protocol(app, http_protocol_cls, ws="none")
+    protocol.data_received(UPGRADE_REQUEST_ERROR_FIELD)
+    await protocol.loop.run_one()
+    assert "Unsupported upgrade request." in caplog.text
+    msg = "No supported WebSocket library detected. Please use \"pip install 'uvicorn[standard]'\", or install 'websockets' or 'wsproto' manually."  # noqa: E501
+    assert msg in caplog.text
+    assert b"HTTP/1.1 200 OK" in protocol.transport.buffer
+    assert b"Hello, world" in protocol.transport.buffer
diff --git a/uvicorn/protocols/http/h11_impl.py b/uvicorn/protocols/http/h11_impl.py
index ce51024fa..932ddf62b 100644
--- a/uvicorn/protocols/http/h11_impl.py
+++ b/uvicorn/protocols/http/h11_impl.py
@@ -147,14 +147,24 @@ def _get_upgrade(self) -> bytes | None:
 
     def _should_upgrade_to_ws(self) -> bool:
         if self.ws_protocol_class is None:
-            if self.config.ws == "auto":
-                msg = "Unsupported upgrade request."
-                self.logger.warning(msg)
-                msg = "No supported WebSocket library detected. Please use \"pip install 'uvicorn[standard]'\", or install 'websockets' or 'wsproto' manually."  # noqa: E501
-                self.logger.warning(msg)
             return False
         return True
 
+    def _unsupported_upgrade_warning(self) -> None:
+        msg = "Unsupported upgrade request."
+        self.logger.warning(msg)
+        if not self._should_upgrade_to_ws():
+            msg = "No supported WebSocket library detected. Please use \"pip install 'uvicorn[standard]'\", or install 'websockets' or 'wsproto' manually."  # noqa: E501
+            self.logger.warning(msg)
+
+    def _should_upgrade(self) -> bool:
+        upgrade = self._get_upgrade()
+        if upgrade == b"websocket" and self._should_upgrade_to_ws():
+            return True
+        if upgrade is not None:
+            self._unsupported_upgrade_warning()
+        return False
+
     def data_received(self, data: bytes) -> None:
         self._unset_keepalive_if_required()
 
@@ -206,9 +216,7 @@ def handle_events(self) -> None:
                     "headers": self.headers,
                     "state": self.app_state.copy(),
                 }
-
-                upgrade = self._get_upgrade()
-                if upgrade == b"websocket" and self._should_upgrade_to_ws():
+                if self._should_upgrade():
                     self.handle_websocket_upgrade(event)
                     return
 
diff --git a/uvicorn/protocols/http/httptools_impl.py b/uvicorn/protocols/http/httptools_impl.py
index 98e0fe2bd..00f1fb720 100644
--- a/uvicorn/protocols/http/httptools_impl.py
+++ b/uvicorn/protocols/http/httptools_impl.py
@@ -141,19 +141,20 @@ def _get_upgrade(self) -> bytes | None:
             return upgrade
         return None  # pragma: full coverage
 
-    def _should_upgrade_to_ws(self, upgrade: bytes | None) -> bool:
-        if upgrade == b"websocket" and self.ws_protocol_class is not None:
-            return True
-        if self.config.ws == "auto":
-            msg = "Unsupported upgrade request."
-            self.logger.warning(msg)
+    def _should_upgrade_to_ws(self) -> bool:
+        if self.ws_protocol_class is None:
+            return False
+        return True
+
+    def _unsupported_upgrade_warning(self) -> None:
+        self.logger.warning("Unsupported upgrade request.")
+        if not self._should_upgrade_to_ws():
             msg = "No supported WebSocket library detected. Please use \"pip install 'uvicorn[standard]'\", or install 'websockets' or 'wsproto' manually."  # noqa: E501
             self.logger.warning(msg)
-        return False
 
     def _should_upgrade(self) -> bool:
         upgrade = self._get_upgrade()
-        return self._should_upgrade_to_ws(upgrade)
+        return upgrade == b"websocket" and self._should_upgrade_to_ws()
 
     def data_received(self, data: bytes) -> None:
         self._unset_keepalive_if_required()
@@ -166,9 +167,10 @@ def data_received(self, data: bytes) -> None:
             self.send_400_response(msg)
             return
         except httptools.HttpParserUpgrade:
-            upgrade = self._get_upgrade()
-            if self._should_upgrade_to_ws(upgrade):
+            if self._should_upgrade():
                 self.handle_websocket_upgrade()
+            else:
+                self._unsupported_upgrade_warning()
 
     def handle_websocket_upgrade(self) -> None:
         if self.logger.level <= TRACE_LOG_LEVEL: