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.
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.