Murray, who lost 6-4, 6-2, 6-2 to Tomas Martin Etcheverry, last went out in the opening round in Melbourne in 2019 when the Scot expressed doubts about his future in the sport before going on to resurrect his career after having hip-resurfacing surgery.
The 36-year-old twice Wimbledon champion has struggled to reach the latter stages of majors in recent years but dragged himself into the third round at Melbourne Park in 2023 with back-to-back five-sets wins.
After his latest defeat, however, Murray said there was "a definite possibility" that it would be the last time he plays on the blue courts of Melbourne.
"Probably because of how the match went and everything, I don't know," he said. "Whilst you're playing the match, you're obviously trying to control your emotions, focus on the points and everything.
"When you're one point away from the end, you're like, I can't believe this is over so quickly, and like this. Yeah, in comparison to the matches that I played here last year, it's the complete opposite feeling walking off the court.
"Wish I involved the crowd more. Just disappointed with the way I played and all of that stuff, so... Yeah, tough, tough way to finish."
