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 at the Allianz Arena to progress to the quarter-finals.
The Barclays 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 Arenal 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 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."
Unlike previous campaigns, all is not yet lost for the Gunners in 2014, though, as they will head to Tottenham on Sunday out to get themselves back in the title race and can look ahead to an FA Cup semi-final against Wigan at Wembley in April.
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.
"He has a hamstring problem that looks quite serious," he said.
"I don't know (how long he will be out for), but for sure he is out (of the Tottenham game on Sunday).
"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."
Arsenal were only able to name six substitutes, with midfielder Ryo Miyaichi part of the travelling group following some late withdrawals, but it was later discovered he was not eligible for the pre-submitted Champions League squad.
"He was not eligible because he was not qualified to play in the Champions League because I wanted to give him out on loan, so we took him out of the list and UEFA informed us today that he is not qualified," said Wenger.
"Because he was on the bench on Saturday (against Everton), naturally he was with us but honestly that did not have an impact on tonight's result."
Ex-Barcelona boss Pep Guardiola felt his side were good value to progress to the quarter-finals.
"The players were very intelligent, the way we played. We wanted to control the game," he said.
"In the first half we only had one chance but we didn't give them any chances, so we played very well in that aspect and we wanted to put a bit more pressure up front.
"Our goal was very good. We then conceded a goal that wasn't so good, we had a few problems for about 15 minutes but we didn't have any big problems in the game.
"We deserve this qualification for the next round."
Guardiola and Wenger did not appear to shake hands again following the final whistle.
However, the Spanish former Barcelona manager insisted there was no bad blood between the pair.
He said: "No problem. As a trainer I respect everything about the opponents."