The Gunners were thumped 4-0 by a well-drilled AC Milan side in the first leg of their Champions League last-16 tie, which all but put paid to any hopes of progress.
Arsenal manager Arsene Wenger has challenged his team to regroup and deliver a performance when they head back to the Stadium of Light for Saturday's late kick-off a week after their 2-1 win lifted them into the top four of the Barclays Premier League.
A place in the quarter-finals of the FA Cup - which is now the only trophy Arsenal have a realistic chance of winning - would certainly be a welcome tonic and renew belief.
"When you are a professional you put the bad things that happen behind you," Vermaelen said.
"We will have to learn our lessons from what happened in Milan, but it is important at times like this to remain mentally strong and focus on the next game."
Arsenal were never in the contest, failing to get to grips with Milan's rampaging front three of Kevin-Prince Boateng, Robinho and Zlatan Ibrahimovic, who all got on the scoresheet.
Robin van Persie had the Gunners' best of their limited chances on 65 minutes, but saw his fine volley saved at full stretch Christian Abbiati.
With no away goal to give some hope of an unlikely comeback, Wenger admitted Arsenal were now all but out of the competition.
While the second leg at the Emirates Stadium in a fortnight is almost redundant, Vermaelen, 26, insists the players owe it to the Gunners' fans to produce a performance.
"The only thing we can do is remember that we've still got another game to go. Now we have to show some pride and give 100% in the return leg," Vermaelen said.
"We have to give something back to all those Arsenal fans who came all the way out here to this stadium, here in Milan, only for us to disappoint them.
"We must think of them now because what happened was not good.
"The only thing we can do is give them a good result in the home game."
Despite a testing playing service, with the turf on the flanks at the Stadio Guiseppe Meazza having only just been relaid, Arsenal were simply not good enough in every department and were not able to limit the damage.
No side has recovered from such a first-leg drubbing in the history of the Champions League.
Midfielder Mikel Arteta called for Arsenal to make an early breakthrough when the teams meet again in an attempt to launch the most unlikely of recoveries.
"I will never say never in football because you never know," he said.
"If we score two goals in the first half at the Emirates then it is game on.
"However, it will be very difficult to get through and we all know that."
Goalkeeper Wojciech Szczesny also feels if Arsenal can come out of the blocks quickly, then there could still be hope.
"It is not impossible to come back, but it is going to be very difficult," he told Arsenal Player.
"We showed [in the 7-1 win] against Blackburn how good we can be if we are on the front foot, and if we manage to score an early goal then anything can happen.
"We have quality attacking players and we can score goals so why not? But we have to realise that it is going to be really, really difficult."
Szczesny urged his team-mated to regroup and deliver a performance when their domestic campaign resumes - with arch rivals Tottenham set to head to the Emirates Stadium on February 26.
"We are full of belief that we can still have a successful season," the 21-year-old Poland international said.
"The Milan defeat is a big blow for us, but I am confident we will pick ourselves up and do our best in all the games we have coming up."