Wenger's fragile, frustrated side hit a new low on Tuesday when they were beaten on penalties by League Two side Bradford after failing to win the Capital One Cup tie in normal time.
The swell of criticism found a new voice in ex-Gunners midfielder Stewart Robson, who branded Wenger "a dictator" and claimed there was a growing rift between the manager and his assistant, Steve Bould.
But Parlour, who unlike Robson played under Wenger - between 1996 and 2004 - says the Frenchman took a democratic rather than autocratic approach.
"Stewart Robson has got his own opinions, but I played under Arsene Wenger and thought he was a great manager when I was there," Parlour told Sky Sports News.
"He was always one of those managers you could talk to. Arsene Wenger is one of those sort of guys who will always try to stick up for his players.
"We would have meetings after games and it would all come out in the dressing room, which (is how) it should be. It is a private matter between the players, the manager and the staff.
"It was quite embarrassing to lose to Bradford, there is no doubting that, but I think he is one of those guys who does criticise people behind the scenes instead of in the press."