City recorded a 2-0 win at Emirates Stadium following an early red card for Vermaelen's defensive partner Laurent Koscielny.
Belgium international Vermaelen, whose compatriot Vincent Kompany saw red for City late in the game, reckons Arsenal's current run of games will be a vital period for the club.
With an FA Cup third-round replay against Swansea on Wednesday evening, and a Champions League knockout tie against Bayern Munich on the horizon, Vermaelen wants to get back to winning ways as soon as possible.
"There are a lot of big, big fixtures coming up against good teams - big games," he told Arsenal Player.
"This [the defeat to City] was the first one, we wanted to have a good start and that is why it is more disappointing we could not get a good result."
"But against Swansea, I am confident the group will respond on this defeat, and I'm confident we can get a result on Wednesday."
Arsenal's fans have been criticised in some quarters for turning on both the players and manager Arsene Wenger at certain stages of the season.
But Vermaelen reserved special praise for the supporters who stuck by the team during the defeat to City, despite the visitors easing to victory.
"That [the fan's backing] is really important and I'm pleased with that," he said. "That can give us a massive boost that they're behind us, and they did that through the whole game."
"It was difficult for us because we had 10 men, and for them as well, but they supported us through the whole game."
The defeat leaves Wenger's side six points off fierce rivals Tottenham in fourth place with a difficult trip to Chelsea following the cup replay with Swansea.
A win against the European champions will put the Gunners right back into the fight for third spot, with their rearranged Boxing Day clash with West Ham taking place the following Wednesday.
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