Robin van Persie capitalised on an early mistake from Thomas Vermaelen to fire United in front after just three minutes with Patrice Evra adding a second before Santi Cazorla netted a late consolation for a below-par Arsenal.
Wilshere, who was making just his second start after recovering from a lengthy lay-off, was dismissed in the second half for a late tackle on Evra, but Wenger thought his midfielder was unlucky to see red.
Asked about the sending off, Wenger told Sky Sports 2HD: "Not deserved. No, he went for the ball.
"I will have to see it again but it didn't look to me at all that he went on purpose over the ball."
Wenger bemoaned conceding the opening goal to United so early on in the game as it allowed them to dictate the match.
"We put ourselves in trouble because most of the problems we had were on our own mistakes when we had the ball and lost the ball, especially the first goal which is important in a game like that," he added.
"It came very, very early and of course when you put Man Utd in a position where they just have to defend and catch us on the counter attack and I think that is what happened."
Wenger insisted he was not bothered to see former Gunners captain Van Persie score against his old employers.
He said: "We don't care who scores the goals, we want to win the game, that doesn't matter."
Wenger admitted he was frustrated by his side's lack of cutting edge in the final third as they struggled to create goalscoring opportunities.
"We had a lot of possession, but not very progressive, but had a lot of possession so it was important to find some space in the final third of the game and not lose the game before that.
"But when you are down 2-0, down to ten men it was very difficult.
"We didn't create a lot and had a lot of the ball."