The Canaries took the lead on 56 minutes through Michael Turner's header. However, Arsenal were handed a lifeline with five minutes left when the assistant referee spotted a shirt pull on Olivier Giroud. Mikel Arteta levelled from the spot, before Giroud's close-range effort and a strike by substitute Lukas Podolski wrapped things up in stoppage time.
"We left it late, and it was of course unexpected to be 1-0 down at that stage of the game because we were on top and missed chances," said Wenger. "Norwich we knew were strong on set pieces and they punished us for that. We needed spirit and also nerves, we have shown both and in the end got the win we deserved."
The Frenchman added: "But credit to Norwich, they have played very well and if they play like that, then they will not go down. They defended well and gave us problems. We missed chances and from then on it was important to show absolute resilience and we did it."
Norwich bitterly protested the penalty decision, which came following a corner and was not given initially by referee Mike Jones until he consulted with Richard West on the far side. Wenger, though, felt justice had been served.
He said: "Honestly, I have not seen it but people have told me it was a penalty. Television confirmed the penalty. Maybe it was not a corner, but they tell me as well it was not a free-kick (for Norwich's goal)."
Chris Hughton felt Norwich had not been given the rub of the green by the officials.
He said: "My first thought is that it was not a corner in the first place, but what I am more aggrieved about is there is contact with Kei, but he swivels and plays the ball.
"You have a linesman who makes a decision from 40 or 50 yards away and the referee who is eight yards away and has the perfect view.
"Their third goal was also offside. I have had a private conversation with the referee, but I am still not convinced."
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- Olivier Giroud