The title holders and two-time defending European champions crashed out at the group stage following a 2-0 defeat to Chile on Wednesday.
After that game at the Maracana, Alonso admitted motivation may have dipped for a side accustomed to so much success.
That was strenuously denied by Arsenal midfielder Cazorla at Friday’s press conference in Curitiba.
"We did not win the games [against the Netherlands and Chile] but there was no lack of hunger, ambition or desire," he said.
Cazorla denied his opinion of Alonso had changed after his remarks, adding: "We have no doubt on Xabi Alonso or any other team-mate. There is no polemic here."
The future of coach Vicente del Bosque is uncertain following La Roja’s dismal displays in Brazil but Cazorla is hoping he stays on.
"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."