The world number two was outclassed in the opening set by the Serb and, although sets two and three were more evenly matched, Djokovic claimed a record-equalling sixth Australian Open title, 6-1 7-5 7-6 (7-3).
With wife Kim expecting their first child back at home, and with his father-in-law Nigel Sears collapsing while watching Ana Ivanovic's third-round match against Madison Keys last week, Murray was keen to get back to his family.
"I'm proud that I got into this position, just quite looking forward to getting home now," Murray said.
"It's been hard. Regardless of today's result, it's been hard. Had I lost in the third or fourth round it still would have been difficult with everything that's happened.
"Kim has been amazing. She's handled everything unbelievably well.
"I have to thank her for allowing me to play and sort of stay here with everything that was going on. But it was tough.
"I think the earliest one [flight home] was at like 1am but I've been held on flights for it feels like five days.
"I've been held on almost every single flight, so the first one out of here, I'm leaving."