"It was an opportunity for us to try and get into the quarter-finals of the competition and we didn't play well enough and we didn't deserve to go through," O'Neill is quoted as saying by Sky Sports News.
"It was really disappointing. We started off brightly in the game but Middlesbrough forced their way into the game and in truth we didn't create enough. Eventually we didn't have enough confidence but not at the start of the game and not on the back of a strong draw on Saturday against Stoke.
"I thought it was quite the opposite but if you're not playing well enough that can drain you and you can start playing the wrong options."
The draw for the quarter-finals will be made on Wednesday.