The world number one guided S8v i erbia to a 2-0 win by beating Cameron Norrie (28) 6-4, 6-4 in the second singles rubber but then told a group of British fans to "learn how to behave" afterwards.
Djokovic was enraged as some fans tried to drown out his victory speech with drums, which the superstar said he felt he had to respond to.
"The entire match pretty much, there was disrespect but it's something I have to be prepared for in the Davis Cup," Djokovic told reporters.
"It's normal that fans step over the line and in the heat of the moment you react too and in a way show that you don't allow this kind of behaviour.
"They can do whatever they want but I'm going to respond to that."
During the match record 24-time Grand Slam winner Djokovic was annoyed by the same fans causing a disturbance and cupped his hand to his ear after winning a point in the second set.
However, his temper boiled over when they would not allow him to speak undisturbed after his convincing victory.
"I was trying to talk and they purposely started to play the drums, to not let me talk," he said.
"They were trying to annoy me the entire match, so we had a little bit of a chat in the end."
Djokovic's victory puts him on a collision course with Italy's Jannik Sinner, whom he beat on Sunday in the ATP Finals to clinch his seventh title of the season.
Sinner beat Djokovic in the group stage of that competition and the pair are set to meet again when Italy face Serbia in the Davis Cup semi-finals on Saturday.
"Third time in a bit more than a week, it's gonna be great for tennis fans and for both Italian sports tennis fans and Serbia, and here also in Malaga," said Djokovic.
"We're kind of developing a nice rivalry lately."
Djokovic said he watched some of Sinner's singles and doubles victories for Italy in their 2-1 triumph over the Netherlands earlier Thursday and continues to be impressed by the world number four.
"He's really confident and playing, as I said, some of the best tennis that we saw him play ever. I'm not playing bad myself. So it's going to be, I think, a great match."
