Scott McDonald scored the winner in the 39th minute, with the Black Cats unable to break down Tony Mowbray’s side in the second half of the fourth-round clash.
“We’re obviously disappointed,” O’Neill told Sunderland’s website. “We didn’t do well enough.
“We were unable to score a goal to give ourselves a chance in the game.
“We had an opportunity to get through to the quarter-finals of the competition and we failed.”
Middlesbrough’s victory ended Sunderland’s unbeaten record at the Stadium of Light this season, and the Black Cats boss urged his side to bounce back immediately from the setback.
“During the course of the season you meet a number of tests and this is the first one,” O’Neill added.
“We have to pick ourselves up, which is easy to say, but we didn’t play well enough and we didn’t give our supporters enough to get enthused about.
“Middlesbrough came with a totally free spirit and enjoyed the game. If they won, great, if not it wouldn’t have been make or break for their season.
“However, for us this was a big night and we’ve failed the test.
“I think you learn more about people in adversity. We need to get a grip of the situation and prepare ourselves for Saturday, it’s a different competition and it’s a big game for us.”
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