The 60-year-old said his side "defended stoutly" as they battled to a hard-fought 1-0 victory over the reigning champions, while insisting they are not safe from relegation yet
O'Neill's side secured a surprise 1-0 victory against the reigning Premier League champions at the Stadium of Light on Wednesday, courtesy of former City midfielder Adam Johnson's goal, and triumphed in similar fashion on January 1 last season thanks to Ji Dong-Won's last-minute winner.
With many suggesting the winger's effort should have been saved by Joe Hart, while a fine performance from the hosts' keeper Simon Mignolet kept the visitors' attack at bay, the Italian labelled his opponents as "very lucky against us".
The Northern Irishman, however, rejected the 48-year-old's suggestions and instead insisted his players were "terrific" and put in their "best performance of the season".
"I'm genuinely not bothered about what Mancini says," O'Neill told reporters. "I have seen it before with other managers.
"I thought we were terrific. We had the more presentable chances. I don’t think anyone would disagree with that.
"Considering the opposition, I would have to say that was our best performance of the season.
"We took a bit of confidence from winning at Southampton into this game. There were times when you have to play without the ball and there are times when you need to defend stoutly – we did both of them.
"Manchester City are a terrific team. I’m told this is the first time that City haven’t won when Carlos Tevez and Sergio Aguero have started together. So it was a great effort by us."
The victory comes after the important win away at fellow strugglers Southampton, and sees the north East outfit jump up to 13th in the league table - seven points from the relegation zone.
The 60-year-old is not getting carried away though, indicating that the unexpected three points are a "bonus" with some tricky fixtures ahead.
"There is a long way to go yet," he continued. "This gives us some points and a day or two to rest now.
"We have tough games against Tottenham (December 29) and Liverpool (January 2), and maybe this will be seen as a bonus."
O'Neill then moved to praise some of the individual performances from Wednesday afternoon, citing goalscorer Johnson and opposite winger James McClean as two stand-out performers.
He added: "James McClean was truly terrific, both offensively and defensively. He is getting back to that sort of form after a pretty difficult time when everyone was talking about second season syndrome.
"Adam is starting to show some of the form that we know he is capable of. He did look a bit stunned that he'd scored. I must admit I wasn't sure myself until I heard the roar of the crowd. Adam was in my way so I couldn't see!"