The Ulsterman, who was replaced by the Italian following his own sacking by the Black Cats in March, described his successor as a "managerial charlatan" following a sustained attack on his regime during his stint at the Stadium of Light.
Di Canio responded in an exclusive interview with Sky Sports News on Friday, instead accusing O'Neill of being the charlatan and decrying his transfer dealings in particular.
But speaking after his side's 3-0 friendly victory over Latvia on Friday night, the new Republic of Ireland manager said: "At the end of the day, it's hardly worth it.
"You would have to go and check, but I don't think Sunderland would concur with his £40million for a start. Even Sunderland wouldn't do that.
"Seriously, one of those people he's talking about [Steven Fletcher] actually, his goals helped Sunderland stay in the league, and Mignolet, they got £10million for.
"I think they owe a debt of gratitude to [Ireland goalkeeping coach] old Seamus McDonagh, who was out there tonight, McDonagh who I think Simon Mignolet - who is playing brilliantly for Liverpool - would say he had a major influence in his career development."
Di Canio, who led Sunderland to Premier League survival last season before being sacked after five games of the current campaign, told Sky Sports News: "I don't know if he knows the meaning of this word charlatan. Probably I can teach him, even if I am not English.
"I respect the opinion of manager Martin O'Neill but the fact that he spoke after six months, not straight away, that proves what kind of level he is. He is not very big.
"A charlatan is a manager who spends £40million to be a top 10 club and then sees the club sink into the relegation zone."