The narrow victory margin would have been far greater but for heroics from Italian goalkeeper Gianluigi Donnarumma and spurned chances, as Italy coach Luciano Spalletti admitted.
Spalletti attributed the yawning chasm between the sides to his players' lack of freshness, but De la Fuente felt that analysis did not give Spain enough credit.
"Football is not only about freshness and fitness levels, but also tactics and technique," he said. "I think we were superior across the board from a footballing perspective.
"Perhaps it even seemed that Italy played badly, but that's because we played very well.
"Italy won the Euro three years ago. We're still a long way off winning the European Championship."
Spain's performance inevitably prompted questions about whether they can win the title.
"I think we're the best in the world in terms of interpreting various match situations," he told reporters.
"Of course, that is really reinforced and strengthened when you win silverware. But I think it's important to really underline the quality of this generation of players, the players that have actually broken into this squad.
"I think the Spanish players are the best in the world."
De la Fuente knows, however, that it is a long road to Berlin and trophies are not won with impressive performances in the group stage.
"Essentially, we haven't yet achieved anything," he said. "OK, we've won some important matches. We have wonderful prospects.
"But football can also be very cruel. So we need to be cautious. We need to be humble. We need to show respect. And if they (the players) are able to understand that, all the better."
