Ozil has found himself under scrutiny of late after a below-par start to the season, and he was widely criticised after his side's 2-0 UEFA Champions League defeat at Borussia Dortmund in midweek.
Wenger defended his record signing in the build-up to Saturday's Premier League encounter, insisting the World Cup-winning German was being made a "scapegoat" for the loss in Europe.
And, speaking after Arsenal's victory at Villa Park during which Ozil return to his favoured central position, the Frenchman singled out the former Real Madrid man for his mental strength, before dismissing suggestions that he had considered dropping the 25-year-old.
"Ozil played today behind their [Villa's] midfield because they make it very tight in the middle," the Arsenal manager explained.
"It was important for us to find him through the lines to [move] the game forward. It worked, but he can play everywhere.
"It was the point to show him that the confidence [in him] is there. He showed he can respond when under scrutiny."
Arsenal blew Villa away in a spell of just over three first-half minutes, in which they scored all three of their goals - with new signing Danny Welbeck opening his account for the club shortly after Ozil's strike.
And Wenger - who confirmed unused substitute Alexis Sanchez was rested, not injured - was pleased with the England forward's contribution.
"[His goal] was similar to the first one he scored in Switzerland [in England's Euro 2016 qualifier earlier this month]," Wenger added.
"He played well today. He had a good all-round game for a central striker."
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