It was a game of few chances but a single Robin van Persie header in the 27th minute proved to be all the action needed to seal a United win against Wenger’s men in Manchester.
The Gunners boss admits that his side were not composed and often rushed through the game, especially during the first half of their face-off with the Red Devils.
"It's difficult to lose the game. We conceded a goal on a set-piece," Wenger told UK newswires.
"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 is now demanding a stronger response and a return to form as the Gunners face the Saints in about two weeks.
“[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."
Arsenal were without Per Mertersacker and Tomas Rosicky who succumbed to a virus that had run through the squad in the build-up to the Sunday fixture.
Wenger brought in Thomas Vermaelen as replacement for the German international and the Arsenal boss had nothing but praise for Belgian defender.
"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."
The defeat against Moyes means that Arsenal suffer their second Premier League loss of the season.