The victory, which took Spain to their second consecutive Nations League final, was a welcome relief for De la Fuente, who had come under pressure after losing his second match in charge, 2-0 to Scotland in a Euro 2024 qualifier in March.
"We just needed time, I have always said this is a process," De la Fuente told reporters.
"It takes time to establish ideas, we were unlucky that day and didn't get a good result against Scotland, but now with more knowledge of each other and more time in training, things are different."
Spain must continue this improvement in order to beat Croatia in the final in Rotterdam on Sunday, Manchester City midfielder Rodri said.
"We have played Croatia quite a few times, they are very competitive as a team, with outstanding individual players who keep pushing till the end," he said.
"We have the opportunity to compete for a trophy, we must not let that slip through our fingers."
