"This team is not capable of doing what Bolton did," said Allardyce. "The one I had at Bolton had a certain way of playing and knew that it was successful. That became a burden for Arsenal and for Arsene Wenger."
Bolton lost just once in six Premier League home games against the Gunners under Allardyce.
"There was a bit of reverse psychology and they found it hugely difficult to beat us," he added.
"Some of their players' body language wasn't great when they ran out at the Reebok.
"But this is a totally different club and a totally different team."