La Roja were hammered by the Dutch side in their World Cup opener last Friday, but the Manchester United man has refuted suggestions that his national team are not as good as the squads that won the European Championship in 2008 and 2012, and the 2010 World Cup.
Mata told AS: "I am more proud than ever to belong to this group, which is like a family. In difficult times, the biggest show their faces.
"Everyone is convinced we can turn this around. The important thing is the confidence we have in the squad.
"We're not dead. Losing was a blow for everyone but we must have the same mentality as through the years."
Vicente del Bosque's side play Chile in their next game on Wednesday.