The defender launched a thinly-veiled attack on his compatriot, in another incident that suggests the 50-year-old has lost the support of the dressing room
The Portuguese trainer had claimed on Friday that he regretted not signing custodian Diego Lopez earlier, with the former Sevilla player becoming first choice between the posts since his January arrival.
"We have to have a bit more respect for Iker. The boss's quotes were not the most suitable," the 30-year-old said to Canal Plus after Madrid's 4-3 win over Valladolid on Saturday.
"Iker is an institution - at this club and in Spain. He has to know that we [the players] and the fans are behind him."
Speculation continues to link Mourinho with the Madrid exit door and a return to former club Chelsea in the summer and Pepe added that his coach's problems were strictly between him and the club's hierarchy.
"We're relaxed. The coach needs to sort it out with the club. We are playing for the shirt," he concluded.
Los Blancos lie second in La Liga, eight points behind leaders Barcelona.