The Gunners saw their 100 per cent home record in the Premier League come to an end on Saturday as Jose Mourinho's side claimed a 3-1 victory in a thrilling game at the Emirates Stadium.
Antonio Valencia pounced on a Laurent Koscielny mistake to put United ahead after only four minutes, before Jesse Lingard finished a fine move involving Romelu Lukaku and Anthony Martial after forcing Shkodran Mustafi to concede possession.
Arsenal piled on the pressure for much of the rest of the game, but Alexandre Lacazette's goal counted for little as Lingard netted his second following more slack defensive work from the home side.
Wenger was proud of the attacking endeavour of his players, but was left angry that their efforts were in vain because of a lack of early concentration.
"We didn't start well at all at the back but overall our performance was, for patches, absolutely brilliant," he told BBC Sport.
"Despite being 2-0 down, we should have come back. We had enough chances. Were we too nervous?
"I think we produced excellent quality and were not decisive enough, neither in our box nor in their box.
3 - Jesse Lingard has scored three goals in his last two Premier League games, as many as in the previous 51 combined. Impression. pic.twitter.com/P10RoZ7hbE— OptaJoe (@OptaJoe) December 2, 2017
"It was a big blow psychologically to be 2-0 down at the start. When you play at home, that cannot happen.
"We played well but there's nothing more frustrating than when you have that quality of performance and nothing to show for it.
"On one side, I feel extremely sorry for the players because their attitude was impeccable until the end. But when you go into a big game, you cannot make the mistakes that we made."
Arsenal had 75 per cent of the possession and mustered 33 shots, but were thwarted by a strong United defence and an exceptional display from goalkeeper David de Gea.
That said, Wenger was amazed they did not make more of the chances they created, especially once Paul Pogba was given a straight red card with 15 minutes remaining.
"It's a mystery [we did not score more] but he [De Gea] was the man of the match by a mile," said Wenger.
Arsenal had a late penalty shout ignored when Matteo Darmian clipped Danny Welbeck, but Wenger suggested it was a decision that was never likely to go their way.
"I don't want to talk about that. We know that we don't get them," he added.