The defending champion lost 6-3 6-7 (4-7) 7-6 (7-1) but does not intend to play another tournament before the season's third Grand Slam on 25 June.
"There is no need for me to panic," he said. "It takes a bit of time to adjust to the grass courts.
"I need a few days to get my movement right and then I'll play better."
Murray is highly unlikely to enter the Aegon International at Eastbourne next week but may feature in exhibition events at Stoke Park or the Hurlingham Club.
First serve pts won
Total pts won
"I'll discuss with the guys over the next couple of days as to what I'm going to do, whether I play one or two exhibition matches next week.
"It's unlikely I would play a tournament but I'll probably try to get a couple more matches. I just need to spend more time on the grass."
Murray, competing on the surface for the first time this year, rarely looked comfortable in his defeat by the world number 65.
Mahut took the first set with one break of serve and although Murray hit back to edge the second, the Frenchman dominated the third-set tie-break.
Although Mahut has never lifted a title on the ATP World Tour, he came within a point of winning Queen's in 2007 - beating Rafael Nadal along the way.
He was also involved in the longest match in tennis history when he lost 6-4 3-6 6-7 (7-9) 7-6 (7-3) 70-68 to John Isner in the first round of Wimbledon 2010.
Interview: Andy Murray
"He's a very good grass-court player," Murray said. "He's been in the final here, he's beaten Nadal and been a point away from winning the tournament.
"He played well today. It wasn't like I went out on the court, got blown away and played horribly."
The only time Murray had fallen before the last 16 in six previous appearances at Queen's was against Janko Tipsarevic in 2006.
But Mahut, who beat Guillermo Garcia-Lopez in the first round on Tuesday, appeared to have made the transition from clay to grass much more smoothly than Murray.
"I have never really had a problem with [the transition] before, but also that's probably one of the toughest first matches I've played here," continued the Scot.
"I did struggle with my movement, especially earlier on in the match. That's something that I will need to improve."
Mahut said: "It was a big advantage [playing on Tuesday]. This was his first match. It's never easy to start on the grass when you played two months on clay.
"Even if he had three or four practice days on the grass, it's not easy. I was ready to compete against a top player. Even if he's world number four, it's not easy to come on Centre Court with everyone expecting him to win."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.