Robin van Persie's first-half header secured victory for David Moyes' men as the Gunners' lead at the top of the Premier League is reduced to two points.
Robin van Persie’s header in the 27th minute proved to be the difference at Old Trafford as the Gunners slipped to their second Premier League loss of the season.
"It's difficult to lose the game. We conceded a goal on a set piece," Wenger told Sky Sports. "In a big game, that made the difference. In the first half I felt we were too nervous and rushed our game too much. In the second half, when we played composed and had a real go and played our usual game, we were very, very, very, very close to scoring.
"We have to digest that and come back in a strong way. The heart and the desire [from the players] was in it, maybe a bit too much in the first half."
Wenger has now called on his players to hit back strongly after the international fixtures as they prepare to face Southampton on November 23.
“[What am I looking for is] the response after the break," he added. "We had to give a lot this week. We played against Liverpool, Dortmund, here today, [but] I think a draw would have been a fair result today."
A sickness bug went through the Arsenal camp in the build up to Sunday's fixture, with defender Per Mertesacker and midfielder Tomas Rosicky both failing to make the matchday squad.
Thomas Vermaelen deputised for the Germany international and Wenger praised the 27-year-old for his display.
"We are quite strong recently on set pieces," Wenger said. "I was surprised that were caught on the near post. I believe Vermaelen had a very good game. He did lead the line very well."