Real fans called for Coach Manuel Pellegrini's firing, the Chilean has the support of Real president Florentino Perez and director general Jorge Valdano. Fans were particularly incensed when Pellegrini took off French midfield star Lassana Diarra in the 70th minute.
"The public was upset because of [Diarra's] exit," he said. "I understand that ... he had a good game. To lose to a team in the third division can't be considered an achievement."
It marked the second year in a row Real lost to a third-level team. It fell to Real Irun last season.
"There's a nice party going on in the locker-room," Alcorcon coach Juan Antonio Anquela said. "We achieved a dream. To beat Madrid is a dream."
Next up: defending champion Barcelona, a 5-0 winner over Cultural Leonesa.