The former Gunners goalkeeper believes the club's supporters do not realise how good they've had it in recent years.
This season has possibly seen more protests against the French manager's continued rule than ever before as another title challenge went up in smoke.
The Gunners were top of the league at the start of 2016 but a run of poor form saw them slip down the table as well as crash out of the Champions League and FA Cup at a relatively early stage.
However, in terms of their Premier League position, the Gunners had their best campaign in 11 years as they leapfrogged arch-rivals Tottenham Hotspur on the final day of the season to finish as runners-up to Leicester City.
Under Wenger, the club have now finished in the top four in every single one of the 20 seasons that the Frenchman has overseen, and they have not had a campaign without involvement in the Champions League since 1997-98.
Seaman, who played 562 times in 13 years at Arsenal, warned his old club's fans that they must not be suckered into thinking that the high standard that has been set under Wenger can easily be replicated once the veteran boss leaves.
The former England number one told talkSPORT: "More and more fans are getting on the ‘Wenger Out’ bandwagon, and I’m just desperate for him to win the league again just to shut everybody up.
"What frightens me, is that if the club don’t go out and buy these players in the summer, and Arsene does leave, where does that leave Arsenal?
"A lot of fans think that the base that Arsene has set is the standard, but it won’t be. It will fall below that if we get a new manager in."
Though rumours about his future have dogged Wenger throughout this year, there appears to be no sign from either the man himself or the Arsenal board that his reign will be cut short.