The 21-year old midfielder netted his first league goal since November 2010 as the Gunners drew 1-1 with West Bromwich Albion on Sunday and despite his drought-breaking strike, Wenger is not expecting him to all of a sudden become a regular scorer.
"I don't think he will ever be a goalscorer," said Wenger.
"He's a player who can create chances and provide for others. In our job it is quite simple: you need players who score and players who give the ball to those who score.
"Jack is more in the second category than the first. But from the second category you want a few goals as well so it is good that he knows he can score."
As for the negative headlines after Wilshere had been seen smoking during the week, Wenger said: "He is an honest lad and when he's wrong he knows it.
"Today the players do not get away with anything - we got away with a bit more. But they know that is the rule of the game and the rules of modern society and they have to deal with 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. At least that (barren run) is done now."
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