Small shareholders represented by the Arsenal Supporters' Trust (AST) have also demanded greater engagement from Stan Kroenke, the American billionaire who owns a majority stake in the club.
Arsenal have not won a trophy since 2005 and have suffered a disastrous week in which they were knocked out of the FA Cup and effectively eliminated from the Champions' League following a 4-0 first leg drubbing by AC Milan in the round of 16.
In an analysis of the club's finances, the AST estimated that Arsenal had around 50 million pounds ($79.4 million)to "spend or to save for a rainy day". It asked whether this was made available to manager Arsene Wenger to strengthen his squad.
"Did the manager have the option to use all or some of these cash reserves in summer 2011 and January 2012, or are resources being held back as a contingency for failure to qualify for the Champions League?", it asked in an online posting.
Faulure to qualify for Europe's premier club competition would cost Arsenal 45 million pounds, the AST estimated.
Arsenal are currently fourth in the Premier League, level on points with fifth placed Chelsea in the battle for the final Champions League slot.
The success of north London rival Tottenham Hotspur, 10 points ahead of Arsenal in third place, has added to frustration among the AST, who represent shareholders owning around 4.5 percent of the club.
"Our wage spend is 40 percent higher than the payroll at another club in north London and Arsenal are in danger of being overtaken more than temporarily by those who spend their wages more efficiently," it said.
Owner Kroenke would attend the monthly Arsenal board meeting on Thursday, a club spokesman said.
It was not clear if he planned to meet anyone from the AST and the club declined further comment on their financial situation ahead of the publication of interim results this month.
Arsenal host Tottenham on Sunday in a game that will dictate the mood at the club for the short term at least.