Goals from Sebastien Bassong and Anthony Pilkington gave the home side all three points.
Craig Gardner pulled one back for the Black Cats, but they were unable to find the equaliser in the second-half.
O’Neill bemoaned the performance of his team after the game:
“We conceded some very poor goals and it gave us an uphill task, but from the moment we conceded the second goal I thought we played very strongly,” he told SkySports.
“In the second half particularly we were really excellent and created some really decent chances. We should have scored two or three in the second half and didn’t manage any.
“But if we show the same spirit and determination as we did in the second half for the rest of the season, we’ll be fine – although if we show anything like the tension that was with us in the first half then it could be a tough battle.
“There’s no point in taking 25 minutes to warm up.
“We started tentatively and conceded an early goal from the first proper attack and it set us on the back foot.
“The second goal was very poor from our viewpoint so that gave is a tough task, but we rose to that task and should have got something out of the game.
“It doesn’t matter whether you’re playing home or away, you’ve got to close down, you’ve got to go and compete, and that’s what we tried to do in the second half, whereas for about 20 minutes in the first half we didn’t do.”