After failing to take any of eight set points in the opening-set tiebreak, Murray faded in the second and will now take a few days' rest before beginning the countdown to the defence of his Wimbledon crown.
"I need to spend time on the courts practising some things," said Murray, who had been on a 19-match unbeaten run on grass. "The difference between this year and last year is obviously I played a lot of matches the last couple of weeks, at the French Open, whereas last year I probably had about a week, 10 days' preparation on the grass before I started here.
"That obviously helped me during the tournament because not all the other players had that. This year it was two days to get ready for the tournament. So obviously I'm going to take a couple of days off now, because since the Monday before the French Open I have played every single day bar one up to now."
First things first. Yesterday's defeat, as irritating as it will have been for Murray, will have no impact on his chances of retaining his Wimbledon title. The Scot lost his opening match at Queen's Club in 2012 and went on to reach the final at Wimbledon, so it's hardly a precursor for doom.
"I played well on grass over the last few years, so I would have hoped to have done a bit better," he said, "but now it's about how I get myself ready for Wimbledon and how I use the next 10 days of preparation on the grass."
Secondly, yesterday's defeat has nothing to do with the capability of Mauresmo to be a success as Murray's coach. The pair have only just begun their partnership and, providing they get on well, are set to agree a long-term deal.
Murray had warned that the better he does in Paris, the harder it is for him first time out on grass, and so it proved. Just like Rafael Nadal - who won a ninth French Open title on Sunday but was eliminated from the Gerry Weber Open in Halle yesterday by Germany's Dustin Brown - Murray looked a little fatigued, his movement on the grass not yet up to scratch after a longer run than usual in Paris.
Still, he ought to have won the first set, having broken in the first game only to hand the break back straight away and then having squandered a 6-2 lead in the tiebreak and four more set points to lose it 12-10.
Murray's backhand was superb but he struggled on serve throughout and Stepanek, a canny operator on a grass court, always looked for a chance to move forward. A break at the start of the second set put him in command and the Czech held his nerve to clinch victory.
Murray will be back at Queen's on Sunday to play his part in the Rally for Bally, the fundraiser in honour of the late Elena Baltacha, who died in May after a short battle with liver cancer.
Murray admitted the break could be a blessing in disguise. "If I had done well and reached the final, I would have taken Monday, Tuesday, Wednesday off probably, so in some ways, it can be good providing I use next week properly. If I get some good practice in and work on the right things, that can obviously help."
Stepanek will take on the seventh-seeded South African Kevin Anderson in today's quarter-finals.
Murray wasn't the only top player to fall by the wayside, as Jo-Wilfried Tsonga was ousted 6-2, 6-4 by the Australian Marinko Matosevic, whose sexist comments about Mauresmo didn't endear himself to many. Stan Wawrinka, the top seed, had no such problems, crushing the former Queen's winner Sam Querrey, of the USA, 6-2, 6-2 while the No.2 seed Tomas Berdych saw off the Frenchman Adrian Mannarino 7-6, 6-4.
Jamie Murray, meanwhile, rescued a disappointing day for the Murray clan as he and Australian John Peers scored a famous victory over the world's top pairing last night.
Murray and Peers beat top seeds and defending Queen's champions Bob and Mike Bryan in last year's Houston final but recently lost to the American twins at the French Open in Paris. They avenged that defeat yesterday with a hard-fought 7-6 (8-6), 7-6 (7-3) victory to move into the quarter-finals.