The manager says he is a "strong believer" in the teenage midfielder but warns that the player must produce strong displays consistently rather than be hyped for one game.
The 18-year-old started the match for the hosts and impressed, setting up the opener for Santi Cazorla, with Tomas Rosicky scoring the second to seal the win.
Speaking after the game, Wenger had kind words for the young German but said that he was not surprised by Gnabry's performance.
"He has had some good games but maybe we were not at home," he told reporters. "He played well at Swansea City, at Crystal Palace, and overall [on Saturday] 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."
However, the Arsenal boss was also keen not to overdo the praise and warned that Gnabry must continue to produce on a consistent basis.
"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," he added. "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."