The north London outfit have not won any silverware since their triumph in the 2005 FA Cup final, but stand on the brink of glory with Hull City awaiting them in the showpiece match of this year's tournament.
And Allardyce, whose side face Arsenal in the Premier League on Tuesday, believes the club's 2006 relocation from Highbury should take much of the blame for the slump.
"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," he is quoted as saying in the British press.
"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."
The spending power of clubs such as Chelsea and Manchester City has seen both surpass Arsenal in the past decade, and Allardyce feels it would take more than £120 million to see Arsene Wenger's men challenging for the Premier League title once again.
"I would say looking at them that it’s a spending problem," he continued. "Can you spend £120-£150m in one year? Because that's what happened at Manchester City and that’s what happened at Chelsea.
"£100m-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."
