The Black Cats travel to Carrow Road to face Norwich on Sunday, and former Canaries boss O'Neill feels they can turn things around after securing just two wins from their last 21 games, starting against Chris Hughton's in-form side.
He also refuses to be affected by the criticism he has received recently.
"Criticism is a major part of the game, so it doesn’t really concern me. You get it everywhere," he told The Mirror.
"It really doesn’t bother me. We need to win some games, but I don’t get worried. No one is immune to it. If Arsene Wenger, only last week, has been told for the second time in a year by his own fans that he doesn’t know what he’s doing, I think we can all accept plenty of criticism."
The former Northern Ireland international is confident in his own ability to manage his team, and feels it is only a matter of time before their fortunes change.
|AWAY DAY BLUES|
|15/2||Norwich are 15/2 with bet365 to beat Sunderland 2-0 on Sunday afternoon|
"A year into seeing the people here, they have a great passion for the club and that is mixed up with a lot of other emotions, blinding frustration and maybe annoyance that they’ve had a lot of false dawns. Nearly 40 years since we last won a trophy.
"I think it weighs on the fans, it’s not weighing on me. It’s been a long time. The main job here is to get a side that can compete in this league."
O'Neill also denied allegations that he's a quitter, claiming that he fully expects to bring the good times back to the Stadium of Light.
"I had five years at Wycombe, four-and-a-half years at Leicester, five years at Celtic, four years at Aston Villa. People say, ‘When things aren’t going so well, he tends to go.’ Well, that’s not actually true," said the Sunderland boss.
"There must be something wrong somewhere that a club of this size can’t go and really compete, and that’s what I want to do. Sometimes, even up here, I’m not sure people realise how big it is. It’s a great club. I believe I am more driven."