Murray, 32, lost to the Frenchman in the round of 64. The former World No. 1 had hip resurfacing surgery at the end of January in London. Monday's match was Murray's first since the 2019 Australian Open, weeks before his surgery.
"I think I did okay. I think there was a lot of things I would like to have done better in the match, but you also have to be somewhat realistic, as well, in terms of what you can expect in terms of how you actually play and hit the ball," Murray told reporters.
Murray said his legs were a little heavier after the match compared to how they would feel if he was playing more.
"Richard, he uses all of the angles on the court. He's one of the best at doing that. So I was having to move quite a lot laterally, and I didn't move forward particularly well," Murray said. "Like when he drop-shotted, there was a few times I didn't even run to the ball, didn't react to it, and that's nothing to do with my hip. That's just me not running for a ball, which I did do that better at the end of the match."
Murray also said he will not play at the 2019 U.S. Open after falling to Gasquet in short order. The three-time Grand Slam champion fell in five sets to Roberto Bautista Agut in the first round of the 2019 Australian Open.
Murray said he was unable to delay his decision to accept a wild card entry to the U.S. Open from the United States Tennis Association.
"I'm not going to play the U.S. Open singles. We were hoping to maybe hold a wild card until a little bit closer to the time to see how I feel and get some matches hopefully and a bit of practice," Murray said. "I didn't want to take a wild card today [Monday] because I just didn't know how I was going to feel after a match. 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 U.S. Open is set to begin Aug. 26. Murray said he will still play doubles and mixed doubles at the Grand Slam. He also said he could participate at next week's Winston-Salem Open.