Goals from Laurent Koscielny, Tomas Rosicky and captain Robin van Persie gave the Gunners a resounding 3-0 lead against the seven-time European champions, but they were unable to grab the fourth goal that would have taken the tie to extra-time and they bowed out of the competition.
Arsenal have suffered from woeful inconsistency all season but Vermaelen is convinced that his team-mates are now producing the kind of performances that show they deserve to be in the Champions League next term.
"If we can play like we did (on Tuesday night), there is no way that we will not be in the top four," the Belgian said. "That performance will give us a boost now.
"We are out of the Champions League but we need to take the great feeling out of this game. It's really important that we qualify for the Champions League.
"I think Arsenal are a team that belongs in the Champions League. We have the quality to do it, that showed in the second leg."