The German teenager was a constant menace to the Tottenham defence and created the opening goal for Santi Cazorla in a 2-0 win.
Gnabry has started only two Premier League games for the London club, but staked his claim with a promising performance on Saturday.
And Wenger is expecting big things from the tricky 18-year-old wideman.
The Arsenal boss said: "He has had some good games, but maybe we were not at home.
"He played well at Swansea, at Crystal palace, and overall today he has shown that he is quality. He had a very good game.
"He is a very young boy, he (was born in) 1995 so that shows you that he is very young and he has the quality. He is bright, he has a good football brain.
"I am a strong believer in Serge, because I integrated him at the start of last season but let's not make superstars with one game.
"The top level is (about) consistency but I believe the ingredients are there. he has to show he can turn up with these performances in every game."
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