Di Canio succeeded O'Neill at Sunderland before losing his job last month.
Commenting on Di Canio's ban on certain foods, including tomato sauce, O'Neill said: "I'm hoping at some stage or another when John O'Shea asks me at the dinner table to pass him the tomato sauce, I will dispose of it immediately. But then if I feel you can't win games without tomato sauce I will empty it on his plate, with the chips.
"John Robertson once said that if every team in Italy has pre-match pasta for their meals, how come three get relegated each year? It's an interesting point. Ability might come into it.
"I'd have loved the opportunity to sign 15 players like he did. I never got that opportunity.
"Sunderland were my team. Absolutely. I was very disappointed at the outcome. I think I would have garnered the five points necessary to have stayed up and the chance maybe to have changed the side in the summer."
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