The Scot teamed up with American Bethanie Mattek-Sands in the mixed doubles, with the pair hoping to win a second straight major title after lifting the trophy at the US Open last September.
They took the opening set against Czech Barbora Krejcikova and Croatia’s Nikola Mektic but the fifth seeds fought back to win 5-7 6-4 10-1 on a deciding tie-break.
Murray said: “They played a really good match. I think we did well, especially Beth, at the end of the first set to turn it around, came up with some amazing points.
“We were a bit unlucky to lose my serve and then I thought the girl started to play a really good match the last quarter of the match and I thought Nikola played a good match from start to finish.
“The tie-break, we kind of got off to a bad start and it got away from us quick, which was a disappointing way to finish the tournament but it happens sometimes.
“We still had a great tournament, to get to the final is an awesome effort and we had a lot of fun along the way. It’s just a shame we couldn’t quite finish it tonight.”
Murray and Mattek-Sands made an inauspicious start, with the Scot dropping his serve in the first game.
It stayed that way until Mektic served for the set at 5-4 and sent down a double fault on the deciding point.
Murray and Mattek-Sands seized their second opportunity with relish, breaking Krejcikova’s serve to take the set as Mattek-Sands threaded a backhand down the line.
It was the Murray serve that proved vulnerable again in the fifth game of the second set, although the British-American pair could count themselves unlucky as the ball kicked up off the net cord and made life difficult on the volley for Mattek-Sands.
The American’s serve was then broken and, although Murray and Mattek-Sands retrieved one of the breaks, Krejcikova and Mektic pushed the match into a deciding tie-break.
That proved to be one-way traffic as the Czech-Croatian duo won the final eight points.