First-half goals from Sebastien Bassong and Anthony Pilkington were enough for the Canaries to see off the visitors, despite Craig Gardner getting a goal back before half-time.
And, with his side now precariously near the relegation zone, the 60-year-old has insisted Sunderland must play with confidence for the full 90 minutes if they are to survive this season.
"I think if we show the same spirit as we did in the second half for the rest of the season we'll be fine, and if we show anything like the tension that was in us in the first, we could be in a big battle." he told reporters.
"We conceded some very, very poor goals and it gave us an uphill task,
|NO FUN FOR SUNDERLAND
|11/4||Sunderland are 11/4 to be relegated with William Hill|
O'Neill was also left facing a nervous wait for an update on an injury to the club's top scorer Steven Fletcher, who was substituted at half-time.
He added: "He's sore, he's with our doctors as we speak, and we'll be able to get a proper update probably on Monday."
Norwich boss Chris Hughton, meanwhile, was full of praise for his players after their recent hectic schedule.
"It's a third game in a week with the same team, I thought we were excellent first half." he said.
"Very difficult to sustain that for 90 minutes, particularly at the time of their goal that gave them a real lift.
"I thought [Adam] Johnson was always a threat, and we had to dig deep in that second half, but as I say third game in a week, same team, really delighted."