Serbia's Djokovic beat the British number one in straight sets and was clearly the better man in a 6-4 6-2 6-3 win.
But he said: "I want to congratulate Andy for a great two weeks, it was really difficult to play against you tonight.
"Hopefully you will have another chance to win a Grand Slam trophy and, with your talent, I'm sure you will."
A disappointed Murray said: "He had an unbelievable tournament and deserved to win.
"Hopefully I'll come back and have more chances in the future."