The Black Cats were only able to take a point from Norwich, who played for more than an hour at the Stadium of Light with only 10 men, as they failed to end their search for first a league victory at the seventh attempt.
O'Neill is now facing a run of games which sees his side face Manchester United, Chelsea, Newcastle and Everton, and he said: "We had an opportunity there to go and try to get three points. It's difficult - it's been difficult all season for us. But we have games still to play, tough matches, every one of them. But the whole league has been tough for us."
He went on: "I wouldn't stop at four - they are all difficult games. This is the league. You play everybody twice, this is the run of games.
"But we had a situation around about Christmas-time when people were showing the fixture list then, and we were able to win back-to-back games against Southampton and Manchester City, so we have to go and do that again."
O'Neill's frustration was all the more acute as his side enjoyed the benefit of three key decisions by referee Chris Foy, two of which were correct and the third more dubious.
Norwich took the lead with 26 minutes gone when Wes Hoolahan headed home from close range after Kei Kamara had helped Robert Snodgrass' corner towards goal.
However, they were dealt a major blow within three minutes when keeper Mark Bunn was sent off for handling outside his box as he blocked Danny Graham's effort.
Sunderland levelled five minutes before the break after Sebastien Bassong was adjudged to have blocked John O'Shea's pass with his arm and Craig Gardner blasted home the resulting penalty, although Canaries boss Chris Hughton insisted Graham should have been given offside before the ball struck the defender.
Hughton said: "The lad has come from an offside position - and that is the same linesman who gave the penalty decision. He has not given an offside and he has given a handball."