As it was, their chances of lifting the trophy in May look extremely bleak now.
Toni Kroos and Thomas Muller but visiting Bayern 2-0 up at the break and although Lukas Podolski pulled one back for the Gunners after the restart, Mario Mandzukic restored the two-goal margin shortly after.
You can find out the match unfolded with our minute-by-minute commentary below.
"I've got a real sneaky feeling for an arsenal victory tonight-not sure over two legs tho but tonight yes!"
"The fans have to believe in the manager. Since Arsene Wenger came to Arsenal he has done a lot for the club and won lots of trophies. We have so much criticism that sometimes you don't see the bigger picture. His record at Arsenal is fantastic. The club has improved in many ways.
"They have a fantastic training ground and new stadium and the team always play in the Champions League. Despite losing to Blackburn the team is going to respond well. The whole team will be desperate to beat Bayern."
"Bayern are favourites, no doubt about that. In two games we will have our chances to reach the next round. You can be sure, we will not sit and wait to find out what Bayern does. We have the quality to stand our ground against them."
"Obviously Arsene sounded very tetchy. I'm sure if he listened back to that press conference, he would regret the way he conducted it.
"But I would like to put a couple of things straight. With the contract situation, I've checked with the press office, He was trying to say there was a story in the national papers yesterday, and not one corporation checked it out with the press office. The truth is that story is not true.
"I didn't like what I heard today. Every half-hour on my drive here, I've heard Stewart Robson quoted criticising Arsene. Stewart is a guy who worked here, and is obviously a bitter guy because he's no longer got employment here. You have to take into account why Arsene is feeling like he is."
ARSENAL: Mannone, Diaby, Rosicky, Giroud, Oxlade-Chamberlain, Coquelin, Jenkinson
BAYERN: Starke, Robben, Shaqiri, Rafinha, Gustavo, Gomez, Tymoschuk
"Took Ramsey eight minutes to mess it up. Quite good by his standards."
"Bayern look like Wenger's old trophy-winning Arsenal teams - tall, powerful, fast, skilful, aggressive, focused."
"Who on earth would put Cazorla on the wing and Ramsey centre midfield against Bayern Munich? Wenger's completely lost it."
"I'm deadly serious about Heynckes to replace Wenger. We should pay him whatever he wants - his Bayern team are magnificent. This is our best team - the culmination of Wenger's rebuilding strategy since the Invincibles. And we're getting humiliated.
"Shocking first half....just shocking. Wenger's wrecking his once-imperious reputation more and more with every day he stays at #Arsenal. So we deliberately blew any chance of the FA Cup for this farce? Shameful management. #WengerOut."
"Arsenal of old would of gotten right amongst Bayern tonight. This team just doesn't have the nastiness needed to win things. For all the flair, pace, skill and technic, you need can't beat a bit of old fashioned aggression."