diff --git a/src/libraries/System.Net.Quic/src/System/Net/Quic/Internal/ThrowHelper.cs b/src/libraries/System.Net.Quic/src/System/Net/Quic/Internal/ThrowHelper.cs
index fa86818619f75c..774d0f71398f4d 100644
--- a/src/libraries/System.Net.Quic/src/System/Net/Quic/Internal/ThrowHelper.cs
+++ b/src/libraries/System.Net.Quic/src/System/Net/Quic/Internal/ThrowHelper.cs
@@ -215,26 +215,4 @@ public static void ValidateNotNull(string argumentName, string resourceName, obj
             throw new ArgumentNullException(argumentName, SR.Format(resourceName, propertyName));
         }
     }
-
-    public static void ObserveException(this Task task)
-    {
-        if (task.IsCompleted)
-        {
-            ObserveExceptionCore(task);
-        }
-        else
-        {
-            task.ContinueWith(static (t) => ObserveExceptionCore(t), CancellationToken.None, TaskContinuationOptions.ExecuteSynchronously | TaskContinuationOptions.OnlyOnFaulted, TaskScheduler.Default);
-        }
-
-        static void ObserveExceptionCore(Task task)
-        {
-            Debug.Assert(task.IsCompleted);
-            if (task.IsFaulted)
-            {
-                // Access Exception to avoid TaskScheduler.UnobservedTaskException firing.
-                Exception? e = task.Exception!.InnerException;
-            }
-        }
-    }
 }
diff --git a/src/libraries/System.Net.Quic/src/System/Net/Quic/QuicConnection.cs b/src/libraries/System.Net.Quic/src/System/Net/Quic/QuicConnection.cs
index 95457e48584077..63be64f12af7f8 100644
--- a/src/libraries/System.Net.Quic/src/System/Net/Quic/QuicConnection.cs
+++ b/src/libraries/System.Net.Quic/src/System/Net/Quic/QuicConnection.cs
@@ -658,14 +658,22 @@ private unsafe int HandleEventShutdownInitiatedByTransport(ref SHUTDOWN_INITIATE
     {
         Exception exception = ExceptionDispatchInfo.SetCurrentStackTrace(ThrowHelper.GetExceptionForMsQuicStatus(data.Status, (long)data.ErrorCode));
         _connectedTcs.TrySetException(exception);
-        _connectionCloseTcs.TrySetException(exception);
+        if (_connectionCloseTcs.TrySetException(exception))
+        {
+            // Observe the exception as the task is used only for internal workings and might not be observed.
+            _ = _connectionCloseTcs.Task.Exception;
+        }
         _acceptQueue.Writer.TryComplete(exception);
         return QUIC_STATUS_SUCCESS;
     }
     private unsafe int HandleEventShutdownInitiatedByPeer(ref SHUTDOWN_INITIATED_BY_PEER_DATA data)
     {
         Exception exception = ExceptionDispatchInfo.SetCurrentStackTrace(ThrowHelper.GetConnectionAbortedException((long)data.ErrorCode));
-        _connectionCloseTcs.TrySetException(exception);
+        if (_connectionCloseTcs.TrySetException(exception))
+        {
+            // Observe the exception as the task is used only for internal workings and might not be observed.
+            _ = _connectionCloseTcs.Task.Exception;
+        }
         _acceptQueue.Writer.TryComplete(exception);
         return QUIC_STATUS_SUCCESS;
     }
@@ -675,7 +683,11 @@ private unsafe int HandleEventShutdownComplete()
         _tlsSecret?.WriteSecret();
 
         Exception exception = ExceptionDispatchInfo.SetCurrentStackTrace(_disposed ? new ObjectDisposedException(GetType().FullName) : ThrowHelper.GetOperationAbortedException());
-        _connectionCloseTcs.TrySetException(exception);
+        if (_connectionCloseTcs.TrySetException(exception))
+        {
+            // Observe the exception as the task is used only for internal workings and might not be observed.
+            _ = _connectionCloseTcs.Task.Exception;
+        }
         _acceptQueue.Writer.TryComplete(exception);
         _connectedTcs.TrySetException(exception);
         _shutdownTokenSource.Cancel();
@@ -850,7 +862,6 @@ public async ValueTask DisposeAsync()
         Debug.Assert(_connectionCloseTcs.Task.IsCompleted);
         _handle.Dispose();
         _shutdownTokenSource.Dispose();
-        _connectionCloseTcs.Task.ObserveException();
         _configuration?.Dispose();
 
         // Dispose remote certificate only if it hasn't been accessed via getter, in which case the accessing code becomes the owner of the certificate lifetime.