The Gunners are on the brink of a UEFA Champions League exit after the first leg of the last-16 tie against Bayern at Emirates Stadium ended in a 3-1 defeat.
But Vermaelen remains convinced his side can overturn that deficit to progress to the quarter-finals.
Manager Wenger has come under fire in the face of another trophyless season at the club and the Belgian centre-back believes the boss deserves a big performance from his side.
The skipper told The Sun: "Of course we owe the manager.
"We want to give him something back as well because he gives us confidence and belief."
In-form Bundesliga leaders Bayern host Arsenal on the back of nine straight wins in all competitions but Vermaelen is determined the Gunners can pull off a shock, recalling last year's near miss against AC Milan at the same stage.
He said: "Of course you go into this game to win and get through.
"Last year against Milan we almost did it and most people thought it was impossible. The players know that and we all believe we can do it now.
"In football anything can happen. It's difficult but we believe - football is a strange sport."
Arsenal's leaky defence has attracted criticism this season and Vermaelen insists he and his fellow stoppers are working hard to tighten up.
He added: "We always take it personally. But you have to keep going and not worry too much about what people say, just work hard on the pitch every day.
"We are working on the defence every day of every week. This latest match with Bayern will be a tough test again."
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Agree with diabolical / shabtastic and outrun on this- hincey