Vicente del Bosque's side were thrashed 5-1 by the Netherlands, before being beaten by Chile on Wednesday night to become the fifth team in a World Cup to be knocked out of the group stage four years after winning the tournament.
"We didn't know how to maintain our hunger or that conviction needed to win a tournament," BBC Sport quotes the Real Madrid midfielder as saying. "The joy and success we've experienced is over.
"Normally cycles come to an end after a defeat. Maybe it would be best to think about making changes."
Meanwhile, Spain boss Del Bosque did not comment on his future after the loss to Chile.