Pérez added: "This was a totally unexpected decision, Zidane informed me of his choice yesterday".
For now, though, the 45-year-old Frenchman will take some time to consider his next move.
I think this team needs to keep winning but I think after three years a change is needed, something different, a different message, different ways of going about things.
Keylor Navas, goalkeeper of the Costa Rican national team and Real Madrid, has expressed his gratitude towards Zinedine Zidane, who left the club on Thursday. Zidane said he had insulted his family.
Zidane was considered one of the all-time greats as a player, his mixture of sublime skill wrapped up in a muscular package driving France to victory in the 1998 World Cup on home soil. Big players need a change.
We have an obligation to return to the Champions League, which is an exciting challenge.
"I want to end this era at Real Madrid on a high". He has never made a secret of his ambition to do so and speculation will now grow that he will succeed Deschamps after this year's World Cup finals.
Zidane took over at Real in January 2016 as Rafa Benitez's replacement after working with the club's Castilla side.
It is a remarkable record, all the more so for a man who before the Kiev final admitted to not being the best tactician.
Blanc has been out of a job for two seasons now, and is said to be keen to return to management if the right offer comes his way in the next couple of months.
"It's a odd moment to do so, I know, but an important one too", he said.