Mourinho leaves Madrid having won one league title, one Copa del Rey and one Spanish Super Cup in a three-year tenure.
Perez defended the coach's record at the club when asked if the Portuguese's time there could be seen as a failure.
He said: "Everything is related to where we came from. We had been eliminated in the last 16 of the Champions League for six years and were not seeded.
"Now we are among the top four teams in Europe, always in the semi-finals or finals. The overall picture is positive.
"If you asked all the clubs in Europe if they'd be satisfied to reach the Champions League semi-finals three years in a row, they'd say yes. For us, it's not enough, because of what we demand. We are always obliged to improve ourselves."
"Right now the club is in the position it should be in. The word failure is not fair, you now need to get 100 points to win this league.
"Last year we were delighted with ourselves, we were playing spectacular football and beat every record.
"This year it has not been enough for us to get to the semi-finals of the Champions League, the final of the Copa del Rey and coming second in the league. That is what makes Madrid such a great club, we are very demanding, our culture is winning."