diff --git a/test/unit/test_backend.py b/test/unit/test_backend.py
index 70f8a5fa8..955b8f725 100644
--- a/test/unit/test_backend.py
+++ b/test/unit/test_backend.py
@@ -345,6 +345,6 @@ def test_too_many_circuits(self):
         with self.assertRaises(IBMBackendValueError) as err:
             backend.run(circs)
         self.assertIn(
-            f"Number of circuits {max_circs+1} exceeds backend._max_circuits",
+            f"Number of circuits, {max_circs+1} exceeds the maximum for this backend, {max_circs}",
             str(err.exception),
         )