A comical error from Thomas Vermaelen allowed former Gunners captain Robin van Persie to open the scoring after just three minutes, before Patrice Evra doubled United's lead in the 67th minute when he rose unchallenged in the box to head home a Wayne Rooney cross.
Two minutes later, Arsenal's hopes of a comeback were dealt a real blow when Wilshere picked up a second yellow having already been slightly fortunate not to be dismissed earlier, although Santi Cazorla did grab a late consolation when he curled home an effort in injury-time.
Nonetheless, Wenger believes Wilshere, who was only playing in his second match since returning from a 14-month injury lay-off, should not have been sent off.
"It was not deserved," the Frenchman said. "He went for the ball.
"His game is commitment. I will have to see the game but it didn't look to me like he went on purpose over the ball."
Wenger added that he said "nothing special" to Van Persie when the pair met and claimed he was not concerned by the fact his former star player scored.
"Honestly that doesn't bother me at all. It doesn't matter," he added.
"What you want is to win the game - you don't care about who scores in their team."
Instead, it was Arsenal's poor fallibilities in defence and attack that really worried the 63-year-old.
"What is most important is that you don't make a mistake at the back, and that you don't give chances away," Wenger said.
"I am disappointed of course, because we had a lot of the ball, but we were not very efficient in our final third or in their final third.
"Then you feel the domination was a bit illusionary - we had a lot of the ball, but they created more chances and deserved to win the game."