Brazilian forward Alemão settled the tie in the 42nd minute, converting after Strasbourg goalkeeper Mike Penders could only parry Florian Lejeune's volley into his path. Goalkeeper Augusto Batalla then saved a dramatic injury-time penalty from Paraguay international Julio Enciso to protect the clean sheet and seal Rayo Vallecano's passage to the UEFA Conference League final in Leipzig on May 27, where they will face Crystal Palace.
Pérez spoke to Spanish media after the final whistle and did not hold back in his assessment of what his team had produced.
"It is the best match we have done since I have had the fortune of managing Rayo."
He acknowledged the mental test of creating chances without reward before the goal arrived.
"When you are generating chances and the goal does not come, your brain connects with situations where you end up punished. Justice was done."
The Enciso penalty — which arrived in the 94th minute with Rayo leading on the night — was the single moment that could have unravelled everything.
"It was a moment where, if they had found the goal, we would have had to hold on against a team with their own fans behind them for four minutes."
Pérez reserved special praise for Argentine midfielder Óscar Trejo, the veteran club captain who has been a constant throughout Rayo's entire European adventure.
"The figure of Trejo is fundamental and this cannot be understood without him. It is impossible to have this run without Trejo. He deserves it more than anyone."
He also addressed the second-half introduction of forward Pacha Espino for midfielder Ilias Akhomach, framing it as a decision made for the moment rather than a judgement on either player.
"These are moments in the season and today it seemed like Ilias was going well. I know what Pacha produces in people. I like to give him his due. He does everything well."
Rayo's appearance in a European final is the most remarkable story in Spanish football this season. A club from the working-class Vallecas district of Madrid, playing their second ever European campaign, will now stand on the same stage as Crystal Palace in three weeks.
Pérez has built something at Vallecas that nobody predicted. Leipzig will be the measure of how far it can go.