Defeats to the Netherlands and Chile mean that the defending champions will not reach the knockout stages of the tournament, but Cazorla was keen to dismiss suggestions from teammate Xabi Alonso that the team had lost its hunger.
"We did not win the games, but there was no lack of hunger, ambition or desire," the Arsenal midfielder told reporters.
"Vicente has been with us for a long time, thanks to him we have achieved a lot of important things. He knows he has our support."
Spain finish off their Group B campaign against Australia on Monday.