Robin van Persie had already scored twice for the Gunners when he appeared poised to tap in winner from close range, but was shoved to the ground by Kyle Naughton. The dropped points mean both Tottenham and Newcastle could leapfrog the Gunners if they win on Sunday.
Wenger said: "Here the whole season we have got zero penalties. It is absolutely amazing, because you see other clubs who have got 10. I don't know (why the penalty was not given), we have to accept the decision of the referee."
Wenger admitted Arsenal had not been "switched on", although their afternoon started so well with a goal from Yossi Benayoun after just 65 seconds.
The Canaries rallied and were level after Wojciech Szczesny spilled Wes Hoolahan's shot before Grant Holt's deflected effort gave the visitors a deserved half-time lead.
Arsenal did come on strong after the break and a brace from Van Persie in the space of eight minutes put the home side back in charge, only for Norwich substitute Steve Morison to make it 3-3 - and the day was further marred by the news that Gunenrs full-back Bacary Sagna had suffered a broken leg which rules the Frenchman out of Euro 2012.
"It is more than frustrating because we were very poor in the first half, not switched on," Wenger added. "The quality of our first half was absolutely not at the level we wanted to play in a decisive game like that.
"In the second half we did very well and created at least 10 chances, but again we did not take our chances. On top of that we gave them a third goal in a situation that was absolutely unbelievable. In the end we got punished for our mistakes.
"We have to analyse the reasons why we were not sharp enough in the first half. There is no obvious reason because we prepared normally as we always do, and maybe subconsciously we would win it. Norwich played well, you have to give them credit, they did well."
Arsenal must now rely on results elsewhere as they hope to cling on to third spot and avoid a potential tricky Champions League qualifier or even dropping into the Europa League, should Chelsea win the European Cup.