The Gunners crashed out on penalties to their League Two opponents, as their poor season continued - prompting some critics to call for Arsene Wenger's head.
The Arsenal Supporters' Trust stopped short of that but insisted the manager needed a helping hand, and called on more money to be spent on transfers.
AST spokesman Tim Payton said: "This is the most difficult time in Arsene's 16 years and both the club and himself need to change direction quickly if his wonderful era is not to end on a sad note.
"The Arsenal Supporters' Trust cannot fathom why £70m was left untouched this summer.
"Arsene needs to get over his distaste for spending and use the resources that, after all, are provided by the hard-pressed fans who watch the team.
"The AST believe a shake-up is needed. We would like to see new, younger blood added to the board, and they also need to exercise more control and direction over Arsene's football strategy.
"One man cannot direct all transfer targets, wages, coaching methods and manage the team at games. It's too much for one man."