After losing the first leg of their last-16 clash 2-0 with the Germans in London last month, it was always going to be something of a tall order for Arsenal to progress to the quarter-finals.
The Premier League side, however, showed plenty of desire, driven on by an impressive display from England World Cup hopeful Alex Oxlade-Chamberlain in the centre of midfield, although club-record signing Mesut Ozil was somewhat subdued and replaced at half-time due to a tight hamstring.
Arsenal recovered from falling behind to Bastian Schweinsteiger's close-range effort early in the second half, 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 after 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. Norway 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 frontman.
"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," the Arsenal manager said.
"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 spoke again about the first-leg incident at the Emirates, where Robben won a penalty and Szczesny was sent off.
"Even UEFA has come out and said that they have to rethink that problem," said Wenger. "First of all, for me, it was not a goalscoring opportunity because if Szczesny is really shrewd, he can get a foul against him as well for a high foot off Robben.
"This situation can be analysed in both ways, where you can as well give a foul against Robben for his foot being too high. If you look again, where the ball goes after the control, you will see that he never had a goal chance because the ball was at the feet of Sagna. So it was never a goalscoring opportunity."
As for Tuesday night's display. 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.
"We had to defend a lot in the first half, but we knew that being in the game at half-time we had a good chance to win the game," he said.
"I believe that in the second half the opportunities were there, but overall over the two games I feel that what made the difference is the decision to send our goalkeeper off in the first game.
"We played a 1-1 tonight and that decision had a huge impact.
"It was on the same player who got a penalty again tonight and that's the regret we have.
"Spirit wise, we have everything until the end.
"Good luck to Bayern, they are a good side but I think they are this season more vulnerable than last year."
Wenger continued: "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.
"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.
"Even at 1-1, you could see they became suddenly nervous, but because we never managed to make it 2-1, of course you could not really see how they would have responded.
"They are a good team, they are a great side with great players. They played well but we still have regrets over the two games."