The Gunners cruised to an easy victory over the Canaries, with Wilshere sending them on their way after 18 minutes when he finished off a marvellous one-touch move in which he linked up with Santi Cazorla and Olivier Giroud.
Mesut Ozil added a second with a header, and, although Jonny Howson pulled one back for Norwich, an Aaron Ramsey strike and a second from Ozil late on ensured the points.
Wenger reserved special praise for Wilshere's strike, though, which marked his first Premier League goal at the Emirates Stadium.
"It was certainly one of the best [Arsenal] goals, one that I enjoyed the most as well because it was a team goal," Wenger said. "It was a great goal. I think we have scored some good goals this season already. All the goals were great, but the first was exceptional because it was improvised, combination play."
Arsenal is now two points clear at the top of the Premier League table as a result of the victory and has have yet to lose in any competition since the opening-day defeat to Aston Villa.
Wenger's side last won the Premier League title in 2003-04 - when Arsenal went the entire season without losing a game - but the Frenchman was quick to shrug off comparisons between his current crop of players and the team dubbed 'the Invincibles.'
"It is a bit early, we are not at Christmas yet. But honestly we have a good attitude and are hungry, with a good solidarity level," Wenger said. "We have quality, but how far we will go is down to how consistent we can be, how much effort we put into every single game and how much we are able not to get into a comfort zone. That is the top level.
"There is a long way to go. We just have to focus on developing as a team and keep the solidarity we have."