The French forward had been strongly linked with a move to the Spanish champions before deciding to sign a three-year contract extension with PSG instead and Perez questioned Mbappe's change of heart.
The Real Madrid president said: "His dream was to play at Real Madrid.
"We wanted to do it last August and they didn't let him leave, he kept saying he wanted to play at Madrid and 15 days before changed the situation."
Perez continued: "This is not the Mbappe I wanted to bring, he is another one, who must have changed his dream.
"He changes, he is offered other things, he is pressured and he is already another footballer.
"There is no-one at Real Madrid above the club. He is a great player, he can win more than others, but it is a collective sport and we have values and principles that we cannot change.
"The Mbappe who was going to come here is not this one. If it is, I prefer him to stay at PSG. I want the one with the dream."
Despite Mbappe's rejection, Real won both La Liga and the Champions League last season with the help of striker Karim Benzema and Perez suggested that the Frenchman's form was why the club did not enter the race to sign Erling Haaland, who has joined Manchester City.
He told El Chiringuito: "We have the best nine in the world and we weren't going to bring in Haaland to have him on the bench, right?
"We have no interest now other than to build the new team with the youngsters we have and some reinforcement."