The Gunners faced the difficult task of having to overcome a 2-0 deficit from the first leg of their last-16 clash in London last month, but they showed plenty of desire to cause an upset and secure an unlikely place in the quarter-finals.
Driven on by an impressive display from England World Cup hopeful Alex Oxlade-Chamberlain in the centre of midfield - and despite a subdued showing from club-record signing Mesut Ozil before he was replaced at half-time because of a tight hamstring - Arsenal recovered from falling behind to Bastian Schweinsteiger's close-range effort on 55 minutes, with Lukas Podolski blasting in a goal against his former club.
There was late drama when Lukasz Fabianski - deputising for Wojciech Szczesny, who had been sent off in the last game - saved a stoppage-time penalty from Thomas Muller for what looked a soft decision for a challenge by Laurent Koscielny on Robben.
Earlier in the second half, the Holland international had fallen in the penalty area under a challenge from Santi Cazorla. Norwegian referee Svein Oddvar Moen - from whom Wenger had called for a strong performance in his pre-match press conference - was not interested and told the Dutchman to get up, but did not produce a yellow card.
Wenger was clearly less than impressed by the antics of the former Chelsea forward, who was the man tripped by Szczesny in the first leg to result in the goalkeeper seeing red.
"Robben is very good at getting the maximum of nothing and he is a great player and as well a very good diver, but it is part of it," said Wenger.
"He is a fantastic player, I would not deny that, he's one of the best players in the world.
"But he gets in front of a player and then he slows down and goes down. He gets the free-kicks.
"That's where we spoke about yesterday that the referee, if he gives him a yellow card on the first one when he goes down, he will not do it again."
Wenger felt his side could have pulled off another shock result as they did last season, when winning 2-0 here, but bowing out on away goals.
"Our defending, our spirit was good. The frustration we had was the last 20 minutes I felt that Bayern was very vulnerable defensively and that we didn't take advantage of that," he said.
"We always missed the first pass, but I felt the situations were there where we could have made more of it.
"At the end of the day we never got them really under pressure."
Wenger revealed Ozil, who had looked refreshed and scored in the 4-1 FA Cup quarter-final win over Everton on Saturday, could be set for a lengthy spell on the sidelines.
"We have to make a scan tomorrow to see how bad it is but he's out for at least a few weeks. I hope it's not too bad," said Wenger, whose side travel to Tottenham on Sunday.
Bayern boss Pep Guardiola felt his side deserved their place in the quarter-finals.
"They (the Bayern players) were very intelligent the way we played. We wanted to control the game," the Spaniard said.
"We deserve this qualification for the next round."