The Black Cats' 1-1 draw with Everton means they have won just four times at the Stadium of Light this year with Blackburn twice, Wigan and Stoke their only victims.
That has resulted in a paltry return of 16 points from a possible 51 in a difficult 12 months on Wearside, and was a major contributory factor in Steve Bruce's departure at the end of last month.
Bruce frequently lamented the lost of strikers Darren Bent, Danny Welbeck and Asamoah Gyan as a factor in that run of results, and his successor as some sympathy with that view.
O'Neill said: "There are a couple of games I have watched back, and you can have a bit of misfortune in some matches.
"I don't know really what it was like at the back end of last season, particularly when they lost a couple of goalscorers in Bent and Welbeck, so that might have had an effect at the time.
"You are where you are and we have to do something about it."
The first opportunity to do that comes on New Year's Day when the Black Cats will attempt to get off to the best possible start, although in the most testing of circumstances.
Barclays Premier League leaders Manchester City provide the opposition having seen city rivals Manchester United close the gap at the top to goal difference after Roberto Mancini's men could only draw 0-0 at West Brom on Boxing Day.
O'Neill knows his side will have to be at their best if they are to get anything out of the game, but having seen them take seven points from a possible 12 from his four games in charge to date - it might have been nine had referee Howard Webb not wrongly awarded Everton a penalty on Monday - they will head into the game with a degree of confidence restored.
Goals have been hard to come by in recent months, although with front two Nicklas Bendtner and Stephane Sessegnon having both scored in the 3-2 win at QPR last Wednesday night, the manager knows the potential is there.
Sessegnon has regularly looked the club's most dangerous player this season, and O'Neill is confident there is more to come from the Benin international.
He said: "That's something he can add to his game. He doesn't have to be absolutely prolific - although we would love that - but it would be nice just to have a few more goals coming from him.
"For all the good work that he does for us, wouldn't that be a fantastic bonus? I think that would give him a big lift as well."