The Gunners were looking to overturn a 1-0 deficit in the second leg at Emirates Stadium but two early goals handed United a huge advantage, and the visitors ultimately ran out 4-1 winners on aggregate.
Wenger could not hide his frustration after the final whistle and conceded the loss was 'hard to swallow' as the club were condemned to a fourth season in a row without silverware.
"It's the most disappointing defeat. The fans were up for a big night and to disappoint people, it hurts really," Wenger said.
"The most difficult thing for me is that we have the feeling that we never played in the semi-final.
"We started quite well but the most disappointing thing was that the game was over before it started. That is hard to swallow.
"We can only look at ourselves. It's very disappointing to fight such a long way and then to give the game away like we did.
"We don't blame individuals but it's like that. We conceded two in three minutes and that's too much against a side that defends well and which likes to counter attack."