The 35-year-old bowed out to 24th-seeded Spaniard Roberto Bautista Agut 6-1, 6-7 (7/9), 6-3, 6-4, but was given a huge ovation by an appreciative Melbourne Park crowd.
Britain's Murray was clearly feeling the effects of his epic five-setter in round two, which started on Thursday but ended in the early hours of Friday.
Now ranked 66th and sporting a metal hip, the former world number one said he took "great memories" from the first Grand Slam of the year.
The three-time major champion admitted having "mixed emotions", saying: "I gave everything that I had the last three matches - I'm very proud of that.
"But I'm also disappointed because I put loads of work into the beginning of this year and was playing well enough to have a really good run, have a deep run."
Murray did not look to make excuses, but said that after two five-setters to get to round three and his early-morning finish against Australia's Thanasi Kokkinakis "my feet didn't feel great".
The epic five-setter in round two had lasted a gruelling five hours and 45 minutes - the longest match of Murray's storied career.
"My legs were actually okay," he said. "They weren't too bad, but I was struggling with my lower back. That was affecting my serve."
Bautista now faces unseeded Tommy Paul of the United States in the last 16 while Murray has every intention of keeping going, even as age and injuries catch up with him.
"I can have a deeper run than the third round of a Slam, there's no question about that," he said.
