Wenger's insistence that securing Champions League qualification trumps winning a domestic trophy caused a stir at last week's Arsenal AGM.
McDermott believes that Wenger's record speaks for itself over the last two decades.
He told The Mirror: "Anyone who says Arsene should be sacked because he has not won a trophy for a few years is talking nonsense.
"The goal for the top teams is getting into the Champions League and Arsene Wenger has done that over the last 14 years. That is phenomenal in itself.
"They want to win trophies, but they always qualify for the Champions League. Arsene will want to win trophies but he has done that early in his career at Arsenal."
McDermott attempts to help extend his former club's seven-year trophy drought tonight when the Royals host Arsenal in a third-round League Cup clash.