La Roja, who won the tournament in 2022-23, entered the contest off the back of a nine-game winning run, but they could not find a route past a stern Serbia outfit, as the points were shared in a goalless draw.
The result has left Spain second in Group 4 of League A on one point, with Denmark moving to the top of the group courtesy of their 2-0 success over Switzerland in the section's other fixture.
An ill-tempered opening 45 minutes produced five yellow cards, while there were also 14 attempts, nine of which came from Spain, but neither team could find the back of the net.
Ayoze Perez had Spain's best chance of the first period, but his effort was saved by Serbia goalkeeper Predrag Rajkovic, before Luka Jovic somehow missed the target down the other end after smart work from Andrija Zivkovic.
Dani Carvajal had a half-chance for Spain early in the second period, but his effort was just over the crossbar, and La Roja were finding Serbia to be a tough nut to crack.
Spain, as expected, were the team pushing as the contest headed for its final stages, with Alejandro Grimaldo drawing a smart save from Rajkovic from a free kick, before the Serbia goalkeeper denied Lamine Yamal 15 minutes from time, with the game still all square.
Luis de la Fuente's side ended the contest with 22 attempts, but just six of those were on target, and Serbia managed to secure a share of the spoils despite only having 28% of the possession.
MAN OF THE MATCH - LAMINE YAMAL
Yamal is already an absolute superstar at the age of 17, and he could potentially become one of the best players to ever play the sport due to his immense ability.
The Barcelona teenager was comfortably the best player on the pitch in this contest, having four shots in total, while he completed four dribbles and finished with a pass success rate of 85%.
It might not have been the result that Yamal wanted, but Thursday's clash was another indication of his sensational quality, and he was clearly the standout individual on the field in the Nations League fixture.
SERBIA VS. SPAIN MATCH STATS
Possession: Serbia 28%-72% Spain
Shots: Serbia 9-22 Spain
Shots on target: Serbia 2-6 Spain
Corners: Serbia 2-9 Spain
Fouls: Serbia 12-12 Spain
BEST STAT
WHAT NEXT?
Both teams will continue their Nations League campaigns on Sunday evening, with Serbia in action away to Denmark, while Spain face a trip to Switzerland.
Serbia will be aiming to build on what will go down as an excellent result for them against the European champions, while Spain will be bidding to return to winning ways after the frustrating draw.