La Roja dominated the possession and created more opportunities during their UEFA Nations League opener, with Lamine Yamal coming the closest to finding the back of the net for the reigning champions.
However, a stubborn defensive performance from Serbia earned them a welcome point, with the Eagles halting Spain's nine-game winning run.
De la Fuente said that his team improved in the second half after a difficult opening 45 minutes, and the head coach refused to criticise the European champions for their failure to secure all three points.
De la Fuente "not worried" by Serbia draw
"We lacked mostly everything in the first half," De la Fuente told reporters when questioned on the clash.
"In the second half, we were better and much improved but lacked effectively up front. We could have done better, players were a little tired, the heat was excruciating, and we ran out of gas.
"I'm not worried, it's almost a pre-season game for us due to the circumstances, still early in the season and the calendar is busy for the players. It's a process, and we will move forward.
"At this stage of the season, there are players who participate more and others less. In October, when they have accumulated more games, we will talk about other things.
"In September there is a lack of rhythm, it's harder to recover. It's a complicated time. We have to value Serbia, who, defensively, had a lot of energy, and we lacked accuracy."
When are Spain next in action?
Spain will continue their 2024-25 Nations League campaign with a clash against Switzerland on Sunday, and they will then be back in action in October at home to Denmark and Serbia.
La Roja have not reported any injury concerns from their game against Serbia, with the withdrawals of Marc Cucurella, Ayoze Perez, Fabian Ruiz, Nico Williams and Dani Olmo all tactical decisions.