Murray let victory against fellow 19-year-old Novak Djokovic slip from his grasp when he lost his serve while leading 4-3 after taking the first set, while Henman served for the match but lost out to Argentine fourth seed David Nalbandian.
"Obviously I was very disappointed to lose that match as I was pretty much on top of him, but I served really badly today," said a philosophical Murray after his third-round defeat.
"But it's been a pretty good tournament for me even though I would have liked to have gone on for longer."
Murray beat world number three Ivan Ljubicic in his second round match, but admitted that a lengthy season may have taken its toll.
"I beat a very good player in Ljubicic, but a combination of mental fatigue and my serve not holding out were the reasons for my defeat.
"Mentally I'm struggling, maybe after playing around 26 tournaments I'm not used to playing all the time at such a high level."
The Scot said that he had been boosted, however, by talking to former England captain and Real Madrid player David Beckham, who had come to see him before the match.
"It was nice to see him as he is one of the biggest sporting icons ever and is so polite and humble. It's good to see the way he has handled all the attention and criticism when I'm not likely to get even a tenth of that in my career."
Henman, who lost in the final of the Japan Open earlier this month, had his fine run halted by the combative Nalbandian after the two had had a minor dispute over a couple of calls during their match.
"It's frustrating but there were a lot of tight points in those last few games," said Henman. "He questioned my sportsmanship, but if we go down that road there is only going to be one winner.
"But I've been playing well over the last few weeks. I've played some fantastic tennis in the two matches I won."