How do I restore backed-up files from an earlier software version?

[AC Question]

I backed up some of my files with the backup and restore tool in Android (Sony Xperia Z) before upgrading it to the latest version (Lollipop). After attempting to restore the files via the same application, I received a notification message which indicates that the files cannot be restored. "Selected backup records cannot be used due to incompatible software versions. Please use a more recent backup file." was the statement that appeared. Are all of my files gone for good or is there an alternative way to recovering them?