The Briton, who lost his opening match at Queen's last week, was beaten 6-7 6-4 10-7 in the Boodles event at Stoke Park, Buckinghamshire.
Murray, who has been seeded fourth for Wimbledon, attempted to play down the significance of this latest defeat - especially as the exhibition format means he will play against world number one Novak Djokovic on Thursday.
"It's always good to get matches in before a big event, especially against a top 10 player so it was a good test," Murray said.
"I was moving much better than I was a week ago at Queen's, I wasn't slipping around as much which will be important for Wimbledon.
"I'm hitting the ball very well and practice has been very good over the last few days.
"I've got another match here tomorrow and then I'll spend two or three days at Wimbledon before the tournament starts."