Wilshere came to the fore in the second half, cancelling out Sergio Aguero's opener before setting up Alexis Sanchez as the Gunners looked poised for the win, only for Martin Demichelis's 83rd-minute header to deny the hosts.
The England midfielder's form had been the subject of plenty of criticism recently, but Wenger claims that the 22-year-old is en route to silencing his detractors.
"He's coming back physically to his level where he can be," Wenger told the club's official website.
"Unfortunately it takes time to find that fraction of a second where you feel you can make a difference and it's so important in the modern game to get away from people when you win the ball.
"It looks like today was the first time he found it on a consistent level through the 90 minutes."
Arsenal sit seventh in the Premier League table with six points from four games.