The Australian was beaten 6-3 6-1 by Mischa Zverev in a second-round match on Wednesday in which he put in a series of half-hearted serves and appeared to be walking off court before the unseeded German had completed his shot.
The 21-year-old, who has had a number of scrapes with tennis authorities over his behaviour in the past, also clashed with spectators before being booed off the court and was subsequently fined $16,500 by the ATP for his behaviour.
Speaking at the same tournament on Thursday, Djokovic described Kyrgios as one of the greatest talents that the game has seen lately, and said he hoped the Australian would stop squandering his gifts.
"He's got huge potential, huge game," Djokovic added.
"I mean he's been doing well, he's around 15 in the world so you've got to give him credit for that, but on the other hand he obviously has life lessons to learn and he's still relatively young and hopefully that is going to happen."
World number two Andy Murray said he would be happy to mentor Kyrgios.
"If he ever wanted to talk to me or ask me anything, I would obviously be open to that. You don't want to see young guys who are in the spotlight, struggling and making mistakes, doing things that ultimately hurt them," the Briton told reporters.
A contrite Kyrgios did apologise via Twitter a few hours after his defeat.
"Not good enough today on many levels," he wrote. "I'm better than that. I can go on about excuses but there are none. Sorry #StillAWorkInProgress."
(Reporting by Ian Rodricks in Bengaluru; Editing by John O'Brien)
