O'Neill, who was confirmed as the Republic of Ireland manager alongside assistant Roy Keane on Tuesday, was sacked by the Black Cats in March after just under two years in charge and replaced with the Italian, who kept them in the Premier League but left in September after failing to record a win in their first five games.
Di Canio had criticised the fitness of the squad when he took over, something to which the 61-year-old took exception, arguing that he "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," O'Neill told the press.
|6/5||Sunderland are 6/5 with BetVictor to be relegated from the Premier League|
"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 triumph over Manchester City - while also progressing to the quarter-finals of the Capital One Cup with victory over Southampton.
However, O'Neill is confident that he could have turned fortunes around at the Stadium of Light if he had been given more time.
"They were my boyhood team so I'm very disappointed [at how it ended]," he lamented. "I'd have loved having the opportunity to sign 15 players like Paolo did. I never got that opportunity.
"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."