Di Canio was sacked by the Black Cats in September, with his side having won just three of 13 matches under his management.
Bardsley was told to find himself a new club after being pictured lying on the floor of a casino covered in £50 notes.
Cattermole rarely featured during Di Canio 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.
Paolo Di Canio: "These two players were rotten - the most unprofessional players I've ever worked with.
"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.
Stoke are ready to offer £5m for Cattermole this week - according to reports in the national media.
