Although the Black Cats came back from 2-0 down for a point, Sunderland have collected just two points from the last 15.
Sunderland's first goal at the Stadium of Light came via the penalty spot and O'Neill believes they should have had a second - claiming Philippe Senderos had handled the ball - suggesting they are not getting their share of good luck.
O'Neill said: "The last four games we have played, we should not have been beaten in any one of them, and I defy anybody to disagree with me.
"We shouldn't have been beaten in any of those games. I suppose we have stopped the run of consecutive defeats but really a little bit of luck, perhaps, might help.
"But most managers would probably say the same thing. We have got to change things ourselves."