diff --git a/server/storage/schema/schema.go b/server/storage/schema/schema.go
index b87b73cc831..00a441a3fc0 100644
--- a/server/storage/schema/schema.go
+++ b/server/storage/schema/schema.go
@@ -73,7 +73,10 @@ func UnsafeMigrate(lg *zap.Logger, tx backend.UnsafeReadWriter, w WALVersion, ta
 	if target.LessThan(current) {
 		minVersion := w.MinimalEtcdVersion()
 		if minVersion != nil && target.LessThan(*minVersion) {
-			return fmt.Errorf("cannot downgrade storage, WAL contains newer entries")
+			// Occasionally we may see this error during downgrade test due to ClusterVersionSet,
+			// which is harmless. Please read https://github.com/etcd-io/etcd/pull/13405#discussion_r1890378185.
+			return fmt.Errorf("cannot downgrade storage, WAL contains newer entries, as the target version (%s) is lower than the version (%s) detected from WAL logs",
+				target.String(), minVersion.String())
 		}
 	}
 	return plan.unsafeExecute(lg, tx)
diff --git a/server/storage/schema/schema_test.go b/server/storage/schema/schema_test.go
index 3d9bd1065c3..e87f0ff5b14 100644
--- a/server/storage/schema/schema_test.go
+++ b/server/storage/schema/schema_test.go
@@ -15,6 +15,7 @@
 package schema
 
 import (
+	"strings"
 	"testing"
 	"time"
 
@@ -218,7 +219,7 @@ func TestMigrate(t *testing.T) {
 			if (err != nil) != tc.expectError {
 				t.Errorf("Migrate(lg, tx, %q) = %+v, expected error: %v", tc.targetVersion, err, tc.expectError)
 			}
-			if err != nil && err.Error() != tc.expectErrorMsg {
+			if err != nil && !strings.Contains(err.Error(), tc.expectErrorMsg) {
 				t.Errorf("Migrate(lg, tx, %q) = %q, expected error message: %q", tc.targetVersion, err, tc.expectErrorMsg)
 			}
 			v := UnsafeReadStorageVersion(b.BatchTx())