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 will now send his international players away to their respective countries keeping his fingers crossed that they return unscathed ahead of a run of games which sees his side face Manchester United, Chelsea, Newcastle and Everton.
O'Neill 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.
"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."