Despite only arriving in the summer, Benitez's future at the club already looks in jeopardy following a sluggish start to the season, with the low point being last weekend's 4-0 El Clasico defeat to Barcelona.
However, some of the blame for Los Blancos' issues have been attributed to Perez's transfer policy and reports he is putting pressure on the coach to select certain players.
After Sunday's 2-0 win at Eibar, Pepe defended both men and insists the pair have the full backing of the the dressing room.
"We didn't expect to have the game we had against Barcelona, but we're with the Coach the President," the defender said. "We have to match the intensity of our opponents. We know we have a lot of quality in our locker, but that alone won't win games.
"The fans have asked us to play for the badge and that's what we'll do.
"The Clasico hurt us a lot, but we have pride and working hard is the only way we'll get out of this situation. We're working hard to get to where we want to be at the end of season."