A brace of goals from Scott McTominay (26) handed Scotland their first win over Spain since 1984 and a perfect start to their Euro 2024 qualification campaign with six points from two matches.
"I’m delighted with the performance," Clarke told Viaplay. "I thought the players were outstanding from first minute to last.
"The dynamic, enthusiasm and quality of the team didn't change. It's a big night, it feels like a step forward, but it's only six points and you don't qualify with six points. One bad game can set you back, so we stay focused and keep our feet on the ground."
Spain had 67% of the possession, but Scotland managed more attempts on goal in the game, nine to the visitors’ eight.
"We didn't have an awful lot of possession, but what we did have, we used very, very well," Clarke said. "The defensive shape's good, the distance between the units was really good, which stops a large part of Spain's game.
"When you look at the stats, you know you've been out-passed, but when you look at the shots on goal, shots on target – it's almost equal. It means we utilised the ball very well when we had it, which is obviously pleasing."
Clarke will take time to digest the result before thinking ahead to Scotland’s next matches in June, away in Norway and home to Georgia.
"I'll have a couple of quiet days to calm down, and then we start preparing for two big games because June could be a pivotal month for us," he said.
No panic from Spain's De la Fuente
Spain coach Luis de la Fuente (61) was left to rue two defensive errors that cost his side but he refused to blame his players for the defeat.
McTominay scored at the start of each half, profiting from a Pedro Porro (23) slip that allowed Andy Robertson (29) to play the ball into his path before Kieran Tierney (25) shrugged off a weak challenge from Dani Carvajal (31) to cross for the second.
Carvajal had replaced Porro at right back during halftime.
"It's a painful defeat," De la Fuente told Teledeporte.
"Analysing the game, I think early on we have done things well enough to change the result. I'll keep those positives, but there's still a lot to improve. I'm happy with the attitude of the boys.
"At this high level, any mistake costs you. But you shouldn't blame the players. It serves as an experience that any small incident tilts the balance of the match."
De la Fuente said the result will not change his plans ahead of the UEFA Nations League semi-final against Italy on June 15.
"Of course, I bet on the players on this list, the same as others who have not been able to come. I bet on them a thousand times," he said.
"You can always change things and improve. You have to work harder. The players have grasped this idea very well and I have seen them identify with it.
"I think we have planted seeds and that the future will bring us better experiences."
Spain started their Group A qualifying campaign with a 3-0 home win against Norway in Malaga on Saturday.
The defeat in Glasgow is their first in Euro qualifiers since 2014, a run of 19 matches in which they claimed 17 wins
