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.
Martin O'Neill: "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.
"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.
"My concern, obviously, is the players going away on international duty. I won't see them for some time and I'm hoping they come back in one piece."