Goals from Richard Dunne and Darren Bent fired Villa into a two-goal lead at half-time before Robin van Persie's penalty double and a Theo Walcott effort secured victory for Arsene Wenger's side, placing them in them in the fifth-round draw where they face either Sunderland or Middlesbrough.
Despite their two-goal disadvantage, the Belgium international believes his side's style of play would always lead to a comeback against Villa.
“It was a bit of a shock to be 2-0 down at half time because if you look at the way we played, we were quite aggressive and had some good opportunities to score, but Villa got a 2-0 lead," Vermaelen told the club's official website.
“I was still confident at half time. We were the better team the whole game, we were never really under pressure.
“You could see that even in the first half we wanted to put them under pressure straight away, we wanted to keep the tempo high when we had the ball and we did that. In the second half we had that little bit of luck to score the goals.”