Murray was trying to reach the last 16 at a slam for the first time since his hip problems began in 2017 but, after threatening another vintage comeback, he fell to a 6-4 6-4 6-7 (1) 6-3 defeat on Arthur Ashe Stadium.
The Scot said: "It's really difficult. I'm surprised I'm still able to compete with guys that are right up at the top of the game.
"Matches like this, I'm really proud that I have worked myself into a position where I'm able to do that. I'm really disappointed that I didn't get over the line today.
"But I get reminded, 'this is the first time you've made the third round here since 2016'. It's been a difficult six years for me. It's been really hard.
"Although I've only made the third round here, I'm really proud of that effort that I put in to get myself back into these positions. I'm hoping that in the future I can go further but, considering, I did all right."
Murray will head home before turning his attention to Britain's attempt to qualify for the Davis Cup quarter-finals in Glasgow later this month and then the Laver Cup in London.
He remains positive, saying: "I'm improving this year. I want to push and see how far I can go.
"That will be motivational for me and interesting to see, because lots of people told me I wouldn't be able to play again, and lots of people told me I'd be able to hit tennis balls but not compete professionally again. That was nonsense, and I want to see how close I can get back to the top of the game.
"We've got a couple of fun team events to look forward to now in the next few weeks, which can help after a loss like today, being around friends and the team environment, so I look forward to that. And then hopefully I continue to play better through to the end of the season."