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Spain won the European Championships in both 2008 and 2012 either side of lifting the World Cup in 2010, only to crash out of the current tournament after losing their first two group-stage games, 5-1 to Netherlands and 2-0 to Chile.
But the Manchester United midfielder, who was part of their squads in both 2010 and 2012 and has been an unused substitute so far in this World Cup, is convinced Spain will be a threat again at Euro 2016.
"I think we will be back," he told The Scotsman. "We have been fighting every two years for the trophy, for the Euros, for the World Cup.
"Unfortunately we have had two bad games and that is the truth. But I think this team can be as successful as we have been in the last six years."
Mata has admitted Spain were fortunate at various points as they won the 2010 World Cup but feels they have not been in the current campaign.
"Of course it is a pity to be out after two games," he added. "We wanted to fight until the end to win the trophy.
"But it shows how difficult it is to win even one [World Cup]. So imagine how difficult it is to win two in a row. To win the World Cup first of all you have to be a good team but you also have to be lucky at some point.
"I think we were lucky in South Africa. We were an amazing team but we were lucky in some moments of games, which we were not in this World Cup. That's football."