The 31-year-old had just succumbed to defeat in the quad wheelchair singles final at Melbourne Park, losing in straight sets 7-5, 6-0 to Dutchman Sam Schröder, in what was his final appearance at the tournament before retiring.
Alcott, who was this week named Australian of the Year for his role in promoting opportunities for disabled people, drank beer from a water bottle as he reflected on his career and legacy during the post-match press conference.
He then got emotional in front of the TV cameras as he read out a text message from Murray.
"I hope he doesn't mind this but Andy Murray just messaged me: 'I don't know if I've articulated that well but you're an absolute rock star and inspiration. Thanks for everything that you've done'," Alcott read.
"That kills me. Makes me want to cry. Special. Like you're just apart of it … they don't even care you're in a wheelchair."
Alcott fought back tears before composing himself to add: “It’s special. It’s like that everywhere. I never thought that would happen. It’s cool. That’s better than winning a tennis tournament.
”That’s a legend of the sport getting around wheelchair tennis. If it’s good enough for someone like that, it’s good enough for everyone."
Alcott, who now hangs up his racket, finished his career with 15 Grand Slams as well as being the only man ever to complete a Golden Slam, winning all four majors and a Paralympic gold medal in 2021.