Murray, who is fourth seed at the All England Club, crashed out of the AEGON Championships in the opening round last week.
And in only his second match on grass before SW19 begins on Monday, the 25-year-old was beaten 6-7 (5/7), 6-4, 10-7 by Tipsarevic amid the grand surroundings of Stoke Park.
Despite his loss to the Serbian world No.8, Murray said his confidence was high.
"I'm hitting the ball very well, practice has been good in the last few days," he said.
"I am moving much better than I did at Queen's and not slipping around as much – that's going to be important going into Wimbledon."
