After a solid win over a Norway side without in-form striker Erling Haaland on Saturday in their first qualifier, Scott McTominay's brace secured a shock 2-0 home win over La Roja at Hampden Park.
De la Fuente -- a relative unknown who has never managed in La Liga -- was promoted to the job after Luis Enrique departed in December following Spain's disappointing 2022 World Cup campaign.
Spain put in a disjointed, wayward performance after falling behind early on, suffering their first defeat against Scotland since 1984 and first loss in a Euro qualifier since 2014.
De la Fuente made eight changes from the side which beat Norway, retaining only goalkeeper Kepa Arrizabalaga and midfield pivots Rodri and Mikel Merino.
The coach wanted to explore his options in only his second match in charge but tinkered too much.
Spain's five substitutions didn't help improve the performance, which worsened as the night went on, with the side lacking leadership.
One of De la Fuente's early decisions was not to rely on Paris Saint-Germain defender Sergio Ramos, 36, who retired from international duty after the coach phoned him to explain the situation.
Veteran defensive midfielder Sergio Busquets also retired after Spain's last 16 exit at the hands of Morocco in Qatar.
"The defeat in Scotland is no accident," wrote Spanish newspaper Marca.
"The national team are showing signs of being stuck in a maze in which there's no exit nearby."
Only one player in the starting lineup, Dani Ceballos, played for Real Madrid, who are second in La Liga, and there were none from leaders Barcelona.
By contrast, only one member of the team which started in Spain's 2010 World Cup final victory did not play for either of Spain's big two clubs -- defender Joan Capdevila, at Villarreal at the time.
One caveat is that Barcelona midfielder Pedri is injured and Gavi came off the bench to play towards the end.
However, while Alejandro Balde and Real Madrid's Nacho Fernandez started against Norway, the current crop of players is lacking some top-level quality.
Espanyol striker Joselu, 33, made his full debut, while Spain's coach handed Osasuna defender David Garcia his first appearance too.
- 'No doubts' -
De la Fuente argued the Scotland defeat was due to one-off mistakes and said the team was otherwise doing well, while Rodri complained that Scotland used time-wasting tactics in the game.
"It's the way they play," the midfielder told Viaplay.
"For me it's a bit rubbish, always wasting time, provoking you and they always fall, for me it's not football.
"For the speed of the sport you have to move on but the referee has to take (action).
"It's a bit frustrating because you want to win and they waste time. It is what it is, they have their weapons, we have to use our weapons."
Despite the defeat, the Manchester City player said he did not want doubts to creep in but acknowledged the team must improve.
"No doubts, we don't want to start now with doubts, please," Rodri added on Teledeporte.
"We're working, trying, we've done many things well. Evidently in football the only thing that counts is the score.
"We have to improve these lapses, individual errors, they have cost us. We have to improve these details."
Rodri's engine-room partner Merino said the squad were still confident in De la Fuente and the new set-up.
"From the start, the coach has given us the tools and the ideas, that we have to be sure of, and we are sure of them," Merino said.
"Obviously there's a lot of work ahead and we have to improve, that is very clear. But the idea is the same, our confidence is still intact, it's a long road, we need to be calm for things to work out."
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