diff --git a/gspread/auth.py b/gspread/auth.py
index 454f4fab..e5547aa2 100644
--- a/gspread/auth.py
+++ b/gspread/auth.py
@@ -386,8 +386,8 @@ def api_key(token: str, http_client: HTTPClientType = HTTPClient) -> Client:
     """
     if GOOGLE_AUTH_API_KEY_AVAILABLE is False:
         raise NotImplementedError(
-            "api_key is only available with package google.auth>=2.4.0."
-            'Install it with "pip install google-auth>=2.4.0".'
+            "api_key is only available with package google.auth>=2.15.0. "
+            'Install it with "pip install google-auth>=2.15.0".'
         )
     creds = APIKeyCredentials(token)
     return Client(auth=creds, http_client=http_client)