Allardyce said, "I hope their players aren't relishing the fact they have got to come and play here and that they are thinking to themselves that it won't be easy."
"It's not so long ago we managed to beat them 2-0, comfortably. That might be on their minds and it will be fresh in our supporters' minds."
"But our past record against them is exceptionally good," added Allardyce. "We have managed to beat them twice at the Reebok and our fans will relish the opportunity to beat them in the FA Cup."
Arsenal manager Arsene Wenger, however, is not fazed by the draw. "It's all right," he said.
"Every draw is OK for us. We'll go there and have good memories of last season and we'll go there and do it again. I don't mind getting a Premier League team in the FA Cup. It is not more difficult than any other division."
Meanwhile, French midfielder Martin Djetou who was released by Bolton last Saturday is interesting French side Strasbourg.