The second leg was a chess match from the off and Bayern didn't seem to know how to approach it - whether they should shut up shop or kill the game off totally.
Arsenal, if anything, seemed even more confused about how to approach the match early on and with the Bayern fans fairly quiet it all contributed to a strangely-muted atmosphere in the Allianz Arena.
In the end it was mission accomplished for Bayern, but not in the way they would have wished.
Arsenal were exceptional defensively and reduced Bayern to a handful of chances. Laurent Koscielny finally reproduced the kind of form that we saw from his last season but has been too often lacking this season.
He took the role of the organiser of the back four - he was clearly in charge; Arsenal need leaders on the field and Koscielny stepped up last night.
I thought Kieran Gibbs was excellent too, not just defensively but going forward as well.
So there were several encouraging signs for Arsenal but at the end of the day, as fantastic a result as it was, they are still out.
Arsenal return to Premier League action this weekend five points off fourth place and I expect them to use their performance in Munich as a springboard for the rest of the domestic season.
If you look at their remaining fixtures - Reading, Norwich, Everton, Manchester United and Wigan at home and Swansea, West Brom, Fulham, QPR and Newcastle away - they are not bad at all.
I'm sure that Arsenal sides of previous years will have looked at those fixtures and thought 'we'll win the majority of those games'.
I'm not sure you can say that this time around but I did see enough at the Allianz to suggest that they will finish very close to the top four, even without Jack Wilshere.
I wouldn't rule them out of qualifying for next season's Champions League just yet.
I think they will win more of their remaining games than they lose if they apply themselves in the same way as they did last night.
Wenger says the fact that there will be no English clubs in Friday's quarter-final draw should serve as a wake-up call but are we really doing something wrong? I'm not sure that we are.
It hasn't been a vintage Champions League season for our sides but every nation goes through difficult years; there are peaks and troughs all the time. Personally, I think it's much too soon to press the alarm bells.
I remember phases when we thought the Italian clubs would go on and dominate Europe but they haven't of late. It's all part of a natural evolution. There's nothing to be particularly worried about.
You have to factor in the luck of the draw, too. Where would we be now if Manchester United had drawn Porto rather than Real Madrid, or Arsenal had drawn Galatasaray rather than Bayern Munich? The chances are we would have at least one club in the last eight.
I think you have to dismiss this campaign as a one-season disappointment.
It's different if English clubs start to under-perform in Europe week in, week out but we're certainly not at that stage yet.
I'm certain that Bayern fans will be pretty concerned by what they saw last night.
They looked good in the first leg at Arsenal, but on the basis of the second leg I can't see them going on to win the Champions League.
They were missing Bastian Schweinsteiger, who is a big player for them, and Franck Ribery, too, but even taking that into account they were thoroughly disappointing and Arsenal managed to expose them defensively on occasions.
If you look at their Champions League results, they've conceded in every game apart from one, which was against Lille - a team that doesn't pose the greatest attacking threat.
So for me, again depending on the draw, you have to feel that Barcelona are the side to beat after that incredible display against AC Milan.
I've thought all along that the Borussia Dortmund - who play a lovely brand of football and have a fresh, vibrant side - are more suited to the Champions League than Bayern.
Given a kind draw it wouldn't surprise me at all if they got to the final.
Jeff's Gem of the Week
I'm going for Barnet's 4-1 win away at Morecambe. You have to say that Edgar Davids - a staggering appointment by the way - has done well since he arrived there. Barnet seem to survive on the last day of the season every single year but this season they've got an opportunity to secure their status a little earlier than that. Davids' love of the game means that he is desperate to be involved in football and he's certainly getting something right at Barnet because Morecambe were on a good run of form, so it was an excellent result. The battle down at the bottom of League Two is going to go right to the wire - it's impossible to predict at the moment. Torquay are falling like a stone and I'm sure Helen Chamberlain is extremely concerned about their future.
Jeff's climbing Kilimanjaro!
Just as Hartlepool have a mountain to climb this season, so has Jeff; he has decided to attempt to climb Mount Kilimanjaro with a couple of ex-footballers - Colin Cooper and Craig Hignett. A couple of years ago Colin set up the Finlay Cooper fund in memory of his two-year son, who tragically choked to death. Together they're aiming to raise money for all children's causes but principally children's hospices.
To find out more check out our Q&A with Jeff by clicking here. The easiest way to donate is to visit http://uk.virginmoneygiving.com/giving/ and search for Jeff's name. Any donations large or small will be more than welcome.