The Gunners have endured a difficult run of games, suffering back-to-back Premier League defeats at the hands of Manchester City and Chelsea in consecutive weekends.
However, Allardyce is certain that his side will lose the match in North London if Arsenal can hit top form.
"If Arsenal are in top form then they will beat us, however well we play," said Allardyce.
"What we have to do is get in among them and stop them playing the free-flowing football they like to play. We saw how Chelsea disrupted them in the first half on Sunday.
"We want to make sure we don't make life easy for them when they are in possession or they can run us ragged. If we can do that and frustrate the crowd then we have got a chance."
The Gunners host the Hammers at the Emirates Stadium in their Premier League clash on Wednesday.