The Gunners have been written off by many after suffering a humbling 6-0 defeat to table-topping Chelsea on Saturday.
That result has left Arsene Wenger's side seven points off the pace in fourth.
They have, however, got a game in hand on Chelsea and eight more fixtures in which to try and claw their way back into contention.
Vermaelen insists there will be no throwing in of the towel at Emirates Stadium, with it important for Arsenal to ensure that they are in a position to pounce if those above them start to wobble.
The Belgian defender told TV Telenet after another disappointing showing against a fellow challenger: "Every game has its own story.
"It's a pity that we haven't played well in the away games against the top teams, but there's nothing wrong with our mental strength.
"There are still eight games to go and in the Premier League anything is possible.
"All of the teams are strong and every team can beat another. We still have to believe in it."