The win completed an impressive group-stage campaign for Spain, who scored five goals without conceding and stretched their unbeaten run to 34 matches.
De la Fuente believed the performance showed the character of his squad after they were tested throughout a physically demanding contest.
"We were pushed to the limit," De la Fuente said. "The players showed great resilience and commitment in a very difficult match."
The victory came at a cost, however, with forward Yeremy Pino suffering what appeared to be a fractured injury that is expected to rule him out of the rest of the tournament. Winger Nico Williams also finished the match with minor discomfort, although the issue is not thought to be as serious.
Despite the physical nature of the game, De la Fuente refused to criticise the match officials. Instead, he focused on Spain's display and pointed out that referees have support from the Video Assistant Referee system to deal with difficult situations.
The Spain coach also highlighted the strength of his midfield options, saying Pedri, Fabian Ruiz, Dani Olmo, Mikel Merino and Martin Zubimendi all offer different qualities and can be rotated depending on the opposition.
While pleased with his team's defensive record, De la Fuente admitted there is still room for improvement going forward.
"Our main objective is to move the ball quicker and play with greater fluidity," he said. "Defensively we have been very strong."
The coach believes his squad are continuing to develop but warned that the challenge will only increase in the knockout rounds.
"I have total confidence in this group. It is a team that wants to keep growing. We are on the right path, but every match from now on will be even more difficult," he said.
Spain will now face the runners-up from Group J in the last 16, with that position set to be decided after the final group-stage match between Austria and Algeria.