The Hammers' boss says the Gunners have landed themselves in this position by continually allowing their best players to leave the club.
Selling Robin van Persie to Manchester United for £24 million was a big mistake by Arsenal, according to the former Blackburn, Bolton and Newcastle manager.
"It’s not surprising because I don’t know where you go and buy a player of Van Persie’s quality unless you’re going to pay more than £24 million," the 58-year-old told The Sun.
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"Everybody says it’s great business in terms of his age but it’s not really great business for Arsene Wenger when he can’t replace the goals that he’s lost.
"When you sell your best players, which is not normally expected of Arsenal, then it is difficult to replace them.
"There is no doubt the players who have come in are very good but are they better than the ones they have sold?
"It’s a big ask, even for Arsene with his huge recruitment policy, to replace those players immediately."
Allardyce has never won away at Arsenal in his managerial career and hopes the Gunners' current lack of confidence can help him change that record on Wednesday night.
"We also hope the disappointment of their 2-1 defeat against Chelsea means there might be a little lack of confidence," he added.
"If that’s the case then we might have a chance of getting a result.
"If Arsenal are on top form, then Arsenal will beat us, no matter how well we play."