"The coach Rafael Benitez has our full support and confidence. He was picked for his professionalism, his achievements, his experience and his ability," said Perez.
Perez, 68, acknowledged "we had a very bad match" against Barcelona, saying he understood the fans' anger.
"Let him work, the victories will come," he added.
Perez said he had given the 55-year-old Benitez his backing immediately after the game and denied he had received requests from players to sack the coach.
"He has a good relationship with the players and he has a good relationship with the board and with me," Perez added.
Former Liverpool and Chelsea manager Benitez has only been in charge for 16 games, but back-to-back defeats now leave Madrid six points behind Barcelona in the title race.
Benitez took over from popular Italian Carlo Ancelotti in June, but despite his many achievements including winning the Champions League in his first season with Liverpool in 2005, he does not have the aura of Ancelotti, who proved adept at managing the egos of the club's many superstars.
Cristiano Ronaldo and Sergio Ramos both campaigned for "Carletto" to continue at Madrid at the end of last season.
The Madrid fans had called for Perez's resignation towards the end of Saturday's thrashing.
And reports in Spain had suggested appointing the hugely popular former French legend and Real Madrid reserve team coach Zinedine Zidane could help Perez ease the fans' frustration with his running of the club.
Zidane, however, played down suggestions he could replace Benitez.
"I am coach of Castilla (the reserves) and Benitez of the first team. Things are fine at the moment," he said.
"Last year, at the end of the season, I had the feeling that I still lacked something to take over the first team.
"I am doing things little by little and I am in no rush. The important thing is to be happy day-to-day with what I am doing."