The Gunners drew 1-1 at the Allianz Arena on Tuesday night, a late penalty save from goalkeeper Lukasz Fabianski ensuring the Gunners at least avoided a second successive defeat against the Germans as they bowed out of Europe 3-1 on aggregate.
However, unlike the scenario when beaten by Bayern at the same stage of the competition 12 months ago, Arsenal's season is still very much alive.
Manager Arsene Wenger will take his squad - set to be without injured midfielder Mesut Ozil as his hamstring strain is assessed - to Tottenham on Sunday looking to close back up on Barclays Premier League leaders Chelsea.
In April, Arsenal will tackle Sky Bet Championship side Wigan at Wembley in the FA Cup semi-finals, with Hull and League One Sheffield United the other teams left in the competition.
Vermaelen said: "The result (against Bayern) wasn't great for us to go through, but you always need to take the positives out of it.
"We worked hard and that is what you need, the spirit in the team is very good.
"We are still up there in the Premier League, we are in the semi-finals of the FA Cup, you can feel the desire in the team that there is still something to play for."
Vermaelen understands Arsenal will be expected to progress through to the FA Cup final, despite Wigan, the holders, having knocked out Manchester City.
"We can't deny that we are the favourites anymore because we are the highest Premier League team, but this is the FA Cup - there is something special about it," the Belgian defender said.
"Wigan go to Man City and knock them out, we got knocked out last year by Blackburn Rovers, who play in the Championship, so we know what we have to do.
"We are the favourites and we have to act like that to get a good result."
Vermaelen was deployed at left-back against Bayern following injury to Kieran Gibbs.
It has been a difficult season for the Gunners captain, who has seen his first-team opportunities limited by a combination of niggling fitness problems as well as the form of regular centre-back pairing Per Mertesacker and Laurent Koscielny,
The 28-year-old, though, intends to continue to work hard at earning his place in the starting XI again.
"It is not easy, but I try to stay positive," he said.
"Firstly, I have been injured in the last couple of weeks, but when the boss needs me, I try to play well.
"I know anything can happen, so I am happy to play when he needs me.
"From my point of view, I hope it is as much as it can be. I work hard for the team and that is the only thing that I can do."
Vermaelen is hoping to be part of the Belgian World Cup squad this summer. The former Ajax defender has, though, found himself linked with a move away from Arsenal given his circumstances on the fringes of the side.
"There has been a lot of speculation, but I can't talk about it because I don't know what is going on," he said.
"My focus is at Arsenal at the moment. There is still a lot to play for - I can't do anything about rumours."