O'Neill, who was confirmed as the Republic of Ireland manager alongside assistant Roy Keane last Tuesday, was sacked by Sunderland in March after just under two years in charge and replaced with Di Canio.
The Italian kept the club in the Premier League, but left the club in September after failing to record a win in the first five Premier League games of the season.
Di Canio also criticised the fitness of the squad when he took over, something O'Neill took exception to, describing him as a "managerial charlatan" who "ran out of excuses".
"It was like a 27-year-old manager stepping in and the first thing you do is criticise the fitness of the team," he added.
"If you've ever seen (O'Neill's former club) Aston Villa play, you’ll see the one thing I pride myself on is teams being fit.
"What's interesting is that when he started, the team supposedly wasn't fit for the Chelsea game. Then the following week when he won at Newcastle, not being fit wasn't mentioned.
"Then about two weeks later they got mauled by Aston Villa and someone asked him about the fitness. Suddenly, he didn’t know where to go, because the team, as it progresses, should be getting more fit."
Under current manager Gus Poyet, Sunderland have won two of their last three Premier League games - including Sunday's 1-0 success over Manchester City - while also progressing to the quarter-finals of the League Cup with victory over Southampton.
However, O'Neill is confident he could have turned fortunes around at the club if he had been given more time.
"They were my boyhood team so I'm very disappointed (at how his tenure ended). I'd have loved having the opportunity to sign 15 players like Paolo did. I never got that opportunity," he added.
"With my managerial record, I think I would have garnered the five points necessary to have stayed up and (deserved) the chance, maybe, to have changed the side.
"They have taken 12 points from 51 since I left."
