Murray, playing his first Singles match in seven months, suffered a 4-6, 4-6 loss in straight sets against Gasquet.
It was in Melbourne where he played his last singles match, losing to Roberto Bautista Agut just days after announcing his intention to retire, so it would complete a remarkable turnaround for the two-time Wimbledon champion.
Murray, 32, said: "Physically, my legs were a little bit heavy at the end of the match in comparison to maybe what they normally would be if you played a bunch".
"I felt like I wanted to be fair, for me to maybe try and get a couple of matches in before making a decision like that".
The Briton returned to action at the Cincinnati Masters after being sidelined since January with a career-threatening hip injury.
While Murray's comeback was cut short, Maria Sharapova can look forward to a tantalising second-round battle with world No. 2 Ashleigh Barty, who defeated the Russian at this year's Australian Open.
Murray also has to search for a mixed doubles partner with less than two weeks to go. Tentative at times, he finished with a respectable 20 winners but struck 28 unforced errors. "I will not play in the singles category in the US Open", said Andy Murray after the match. I didn't want to take a wild card today because I just didn't know how I was going to feel after a match.
By Tuesday, Murray had realised he had overlooked an ideal opportunity to prove his match fitness in NY, with three best-of-three sets qualifying matches for the grand slam event likely to have proven a flawless test of the state of his game.
The US Open's wild-card timing led Murray to decide against playing in NY. Australian Nick Kyrgios slammed a ball skyward in a moment of distracted anger to earn a warning but buckled down to post a 7-5, 6-4 win over Italian Lorenzo Sonego. In the women's draw at the ATP-WTA event, 2011 victor Maria Sharapova, who last played here five years ago, came back from a pair of first-round defeats at Wimbledon and Toronto, defeating Alison Riske 6-3, 7-6 (7/4).