Arsene Wenger’s men looks odds-on to play a role in potentially finishing in top spot this term, but suffered a capitulation and are now in danger of dropping out of the top four.
Allardyce has stated that the North London club’s expenditure on new players simply must increase if they are to compete with the likes of Chelsea and Manchester City.
“I still go back to the fact that Arsenal’s building of the Emirates is one of the main reasons why they have not won another trophy or won the league since,” the Hammers boss told The Mirror.
“They haven’t had the spending power to sustain what they had before. They used all the money to build the stadium which limited their spending. So I’d say that was the start of what they haven’t been able to recover from.
“I would say looking at them that it’s a spending problem.
“Can you spend £120-£150m in one year? Because that’s what happened at Manchester City and that’s what happened at Chelsea.
“One hundred million pounds-plus in one year. Is that within the capabilities of Arsenal’s spending power at the moment?
“I would say probably not because they are in a position where they run that club in that particular way.
“They obviously give Arsene as much as they can but I don’t think they can give as much as a Manchester City or probably a Chelsea can do.”
Arsenal need to win their remaining games to ensure a top-four finish, as Everton are hot on the London club’s heels.
Wenger’s men can end their nine-year trophy drought this term also, with an FA Cup final against Hull to participate in.