Novak Djokovic locks Serbia's win over Great Britain at the Davis Cup Finals
Britain lost the quarter-final 2-0 as Cameron Norrie was unable to inflict a rare defeat on the world number one.
"You should learn how to show some respect," Djokovic told the fans.
Jack Draper was beaten 7-6 (7-2) 7-6 (8-6) by Miomir Kecmanovic in the opening match of the best-of-three tie.
That result meant Norrie had to beat 24-time Grand Slam champion Djokovic for the first time in his career.
But Djokovic showed his class as he cruised to a 6-4 6-4 win and set Serbia up for a semi-final against Italy on Saturday.
After an assured and drama-free performance, Djokovic had the spiky exchange prior to his on-court interview, challenging the small number of British fans who act as the team's band.
He had celebrated at the end of the first set by blowing a kiss to a British supporter heckling him and also cupped his ear in their direction at the end of the match.
"It's normal that sometimes 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," Djokovic said.
"They can do whatever they want, but I'm going to respond to that. That's what happened.
"Huge thanks to all the fans who made the big effort to travel out there and create a brilliant atmosphere for the players," said Murray, who added the Davis Cup would not be the same without them.
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