Di Canio was sacked by the Black Cats in September, with his side having won just three of 13 matches under his management.
Bardsley publicly got on the wrong side of Di Canio during the Italian's turbulent stint in charge at the Stadium of Light.
The former Manchester United defender was told to find himself a new club after being pictured lying on the floor of a casino covered in £50 notes.
Meanwhile, Cattermole rarely featured during Di Canio's reign because of injury troubles, but the former West Ham United striker believes that the 25-year-old's poor attitude had a detrimental effect on the rest of the squad.
"These two players were rotten - the most unprofessional players I've ever worked with," Di Canio told The Sun.
"The reason Sunderland stayed up [last season] was because Cattermole was injured and Bardsley played very little."
Cattermole and Bardsley are now both first-team regulars under new Sunderland manager Gus Poyet.