If you happen to get an error message like this from a BIG-IQ backup look for an orphaned ucs file in /var/tmp. Once the orphaned ucs file is removed the backup should complete successfully. The message itself is true, that directory does not exist (on my BIG-IPs or BIG-IQ anyway), but seems to have northing to do with the cause of the error.
Error occurred during backup/restore operation on 00.00.00.00: /mgmt/tm/shared/sys/backup not found
Thanks for the heads up @ted . For the message itself, would you mind reporting that into a support ticket if you have a moment? This would help in getting it clarified and accurate in future versions.