The Canaries recorded their first league win under new boss Chris Hughton after producing a hard-working display to capitalise on a lacklustre performance by the Gunners.
Grant Holt's first-half goal, coming after goalkeeper Vito Mannone had spilled Alex Tettey's 25-yard effort, proved enough to condemn Arsenal to a second defeat in their last three Premier League games.
The Gunners are now ninth and have work to do simply to get back into contention for the top four, nevermind reeling in Chelsea.
"The gap is very unpleasant," Wenger said. "We had an opportunity that Tottenham could win and we could win, and we both lost. That of course makes the gap a lot bigger.
"You cannot say you do not worry about that, but what is more disappointing is that we could not score. After we went 1-0 down we had the ball for 70 minutes and could not score a goal."