The Gunners made it six wins in a row with a 3-2 triumph over Bob Bradley's side, but they had to see out the final 20 minutes with 10 men after Xhaka was given a straight red for a challenge on Modou Barrow.
Wenger believes that Jonathan Moss's decision was harsh, but revealed that he would not challenge it due to the nature of the offence.
"No [we will not appeal the decision]. It looked harsh to me but it was a deliberate foul. It looked a 'dark yellow' but the referee went for bright red," he told reporters.
The victory saw Arsenal move joint top of the table, only behind Manchester City on goal difference.