A below-strength Real side fell 2-1 at Celta in a last-16 first leg on Wednesday, and although they are still expected to progress to the quarter-finals next month, the defeat raised further questions over Mourinho's stewardship of the team.
"We have the best coach in the world with an impressive track record, who always demands the very best from his team," construction magnate Perez, who brought Mourinho to Spain in 2010, told a club event on Saturday.
"He has been on the receiving end of unfair criticism and damaging comments and some have affected his dignity as a person.
"Mourinho has my recognition, my confidence in his work and my affection."
The champions trail leaders Barcelona by 11 points in La Liga, and their sixth defeat in all competitions, more than they suffered in the whole of last season, caused Mourinho to again question the commitment of his players.
Local media have written stories about strained relations between the former Chelsea and Inter Milan boss and some players as well as the club's board.
Despite having a contract until 2016, Mourinho's future beyond the end of the season has been the source of constant speculation over the last couple of months as their campaign has stuttered.
"I don't think a coach should comment on what his president says," Mourinho told a news conference on Saturday.
"He should draw his own conclusions but he shouldn't make any public comments. We have spoken this morning, and that is that. I appreciate it."
Real, third in the standings, resume their pursuit of Atletico Madrid and Barcelona, who play at the Nou Camp after struggling Espanyol have visited the Bernabeu on Sunday.
With Gonzalo Higuain still out injured, Mourinho has a problem up front after France striker Karim Benzema limped out of Wednesday's game in Vigo with what appeared to be a foot problem.
"I don't think he will be fit to play tomorrow," Mourinho said of Benzema.
"A player who leaves a game injured shouldn't be ready to play again two days later. We have problems up front with Higuain out and I would like Karim to be available if possible."
Leading scorer Cristiano Ronaldo could play in a central role, while youth team products Jose Callejon and Alvaro Morata offer further options.
Real are five points short of second-placed Atletico, but 21 ahead 19th-placed Espanyol. (Reporting by Mark Elkington, editing by Ed Osmond)
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