El Grana secured their La Liga survival on the final weekend with a 1-0 win over Real Valladolid, but Alcaraz believes that the club "needs a new face" to move forward.
"Personally, I'm very happy to have stayed up. I'm delighted for everyone at the club and the fans," he told reporters at a press conference.
"But I think the club needs a new face. I don't want to take advantage of a moment of success.
"You work hard for 11 months and it comes down to one game. But I thought we played with character and clawed our way to safety."
Alcaraz took charge of Granada in 2013.