Djokovic had dropped just four games across his previous two meetings with compatriot Lajovic, but the world number one squandered several chances to get past his opponent on Friday, converting just one of 16 breakpoints as he fell to a 6-4 7-6(6) defeat.
The loss is Djokovic's second early exit from a tournament in as many weeks, following his third-round defeat to Lorenzo Musetti at the Monte Carlo Masters last week.
"Lajovic played well. On the other hand, I played much worse than I wanted to," Djokovic told reporters after the defeat in Banja Luka, Bosnia and Herzegovina.
"I cannot win matches against opponents who are this solid on this surface by playing like this.
"I didn't feel well on the court, my legs were slow and my footwork was torpid, many missed shots, totally without direction. I played well at times but I played noticeably under my level."
With Rafa Nadal having skipped a string of clay tournaments due to injury, Djokovic will be looking to build momentum ahead of the French Open where the Serbian will target a 23rd Grand Slam to go ahead of the Spaniard.
The French Open, the second Grand Slam of the season, begins on May 28.
"I hope to get into tip-top shape for Roland Garros. I want to play my best tennis there," said Djokovic, who has also been struggling with an elbow injury.
"The conditions are totally different there in comparison with Monte Carlo and Banja Luka. There are still several weeks to practice and play.
"In the previous seasons, I've always had an unsatisfying and slow start on clay and then played much better tennis in the final stages. I hope to repeat the same pattern this year."
