"If you have a tiger as your mascot you have to keep him tied up to stop him eating your neighbour's daughter," said club member Rafael Vareos who prompted catcalls and whistles from the largely pro-Mourinho crowd.
The colourful and combative Portuguese coach, who joined the Spanish giants from Inter Milan at the end of the 2009/10 season, has repeatedly clashed with officials and rival coaches and has created a siege mentality around the club by suggesting there is a conspiracy favouring bitter rivals Barcelona.
During a Spanish Super Cup match against Barca last month, he jabbed a finger into the eye of the Catalan club's assistant coach Tito Vilanova during a mass brawl, for which he faces disciplinary proceedings.
Mourinho won a power battle with Real director general Jorge Valdano, who was sacked in May, and has been handed enhanced powers by president Florentino Perez.
Perez has overseen the spending of hundreds of millions of euros on players and coaching staff as he bids to win a 10th European title.
Vareos told assembly delegates the decision to give what he called "absolute power" to Mourinho was dubious and the pictures of the finger in the eye that flashed around the world were bad for the club's image.
"Mourinho is not a Madridista he is a Mourinhista," Vareos said.
Juan Miguel Nogues, another club member, added: "Mourinho's is not the image of the Madrid family. It's not the one Madrid should be projecting."
Construction magnate Perez has consistently backed his controversial coach.
He told delegates on Sunday the club had "the best coach in the world", although he admitted the eye poking incident "was not good".
"Where does it say that when we suffer from poor refereeing we cannot criticise it?" Perez asked.
"We have the best coach. There are people influenced by the media but they should not let themselves be fooled."
Real are one of four Spanish top-flight clubs that are owned by their members, along with Barca, Athletic Bilbao and Pamplona-based Osasuna.
