Wilshere risked the wrath of manager Arsène Wenger last week after pictures emerged of him smoking a cigarette on a night out.
He experienced a wayward first-half at the Hawthorns on Sunday before his deflected effort secured a 1-1 draw to take Arsenal back to the Premier League summit.
Wenger hopes Wilshere has learnt his lesson.
"Today the players do not get away with anything - we got away with a bit more - but they know the rules of the game and the rules of modern society and they have to deal with it," he said in reference the negative headlines involving Wilshere.
"He is an honest lad and when he's wrong he knows it. But what is more interesting for England and for Arsenal is that he shows the right response on the pitch.
"He had a difficult first half where he was fouled a lot but showed he has character and kept going.
"He has character as well. He doesn't give up, he continues to play his game."