The Black Cats saw their winless run stretched to eight games on Saturday as an own goal from Titus Bramble handed table-topping United all three points at the Stadium of Light.
Another setback leaves O'Neill's side precariously perched just above the drop zone, but he is confident that his players can steer a course to safety.
He told Sky Sports: "Confidence is a major thing in the game and we are striving for it, but I thought the players can take a great deal of confidence from that second-half performance.
"We have to go and put it right, and we intend to do so. There is a determination in that dressing room to get the points. Nothing is too easy in this game, but we are up for the challenge."
O'Neill concedes that Sunderland started slowly against United, which ultimately cost them dear, but feels the manner in which they responded after the break 'bodes well'.
He added: "I thought we were tentative in the first half, a little bit nervous, a bit wary of the quality of the opposition. I thought we maybe gave them a little bit too much room.
"I thought in the second half we started the game and we put absolutely everything into the match, everything we had. It certainly wasn't through a lack of effort, but Manchester United are a very fine side. The second half, I was very pleased with the team indeed.
"I would have liked us to have done better in the first half. It's very hard to keep a performance level like that, but we did in the second half.
"It's difficult to keep that intensity up for 90 minutes against anyone, never mind the best side in the league. If we had been a little bit less tentative to begin with, that might have borne some fruit. That said, I was delighted with the effort of the team and it bodes well."