The Segunda B side, from a satellite town to the south of Madrid, tore apart their near neighbours and could have won by a larger margin as they condemned the nine-times European champions to a third defeat in five outings on Tuesday.
"Go now!" sports daily Marca blared on Wednesday's front page, alongside a photograph of a shattered-looking Pellegrini.
Madrid-based AS led with "Ridicule of the century" while Barcelona-based Sport wrote: "This is the beginning of the end for Pellegrini."
After the game, Real's Chilean coach brushed away questions over whether he would consider resigning and club director general Jorge Valdano said it was important everyone stood together.
Team captain Raul echoed Valdano's calls.
"We win and we lose together so absolutely everyone is to blame," the striker told reporters.
"The display we put on isn't the one the club deserves, or one that sits well with our history. We ask for forgiveness and remind people the tie isn't over yet.
"If there is a club that knows about comebacks it is Real Madrid."
MOTIVATION QUESTIONED
Daily El Mundo spread the blame beyond Pellegrini and questioned the motivation of Real's players saying: "None of them were able to replicate the exceptional work of Alcorcon: the commitment, the pressuring, the pace and the goals.
"Alcorcon showed all the properties a fan would want to see in their team."
The return leg is at the Bernabeu in two weeks and Alcorcon coach Juan Antonio Anquela -- who was being dubbed 'Anqueloti' in the media -- fought to keep the result in perspective while fans celebrated on the pitch outside.
"We haven't achieved anything yet. Real are capable of putting five past anyone," he told reporters.
Pellegrini does not have the luxury of time to put things right. He faces a flurry of high-profile matches before trying to prevent a second consecutive Cup exit to a Segunda B side in the Cup.
Real were embarrassed by Real Union in the last season's competition.
He has a second city derby at home to Getafe in La Liga on Saturday, a trip to AC Milan in the Champions League next Tuesday, and then a third local derby at Atletico Madrid in the league.
