Wilshere showed his immaturity with a reckless challenge on Nikola Zigic in the closing stages which earned him a straight red card and a three-match ban.
Wenger had talked about the need to clamp down on such tackles in his programme notes, and accepted the 18-year-old could have little complaint.
"He mistimed his tackled and got a red card, which he deserved," said the Arsenal manager.
"Jack has acknowledged he deserved it, but he did not spend his whole game trying to kick people, he was one of the best players on the pitch.
"It was more of frustration and did not want to hurt the player, but we do not complain about the red card."
Wenger accepted Wilshere's rash actions will grab the headlines, but maintained the teenager was on the right path.
"Wilshere is a complete player. He played defensively well, offensively well, and overall he had a very influential game," the Arsenal manager said.
Wenger, though, understands better than most the need to keep on top of such incidents.
He said: "We are the team who has the most fouls committed against them, and I encourage our players to play football.
"We got a red card and deserved it. What can we do about it now? Nothing else.
"Wilshere will be suspended for three games and will be punished. I have spoken with him about it already. He said he mistimed his tackle, touched Zigic on the ankle and deserved a red card."