"Any loss is a bad loss. There is no question about it," the Serb said after his 7-6 7-5 2-6 3-6 6-2 defeat that denied him back-to-back US titles. "I'm disappointed to lose the match.
"I had a great opponent today. He deserved to win this Grand Slam more than anybody, I'm sure, because over the years he's been a top player. He's been so close, lost four finals. Now he has won it, so I would like to congratulate him.
"Happy that he won it."
The long-awaited victory made Murray the first British man to win a singles Grand Slam title since Fred Perry 76 years ago.
Djokovic, who is one week younger than fellow 25-year-old Murray and friendly off the court with a rival he has known since junior tennis days, welcomed Murray to the Grand Slam club after the Scotsman's triumph.
He walked around the net to give the dazed Murray a hug and a pat on the back after surrendering the nearly five-hour match with a forehand blasted long.
Having fallen short in his first four Grand Slam finals, Murray was denied another crack at a maiden major title by Djokovic at this year's Australian Open, when the Serb won their semi-final in another epic duel that lasted nearly five hours.
The prospect of a fifth final loss for Murray loomed on Monday when Djokovic mowed through the third and fourth sets to take the match into a decider, but the Serb stumbled with an early double-break of serve from which he was unable to recover.
In contrast to Murray's long wait, Djokovic tasted Grand Slam success at a tender age when he won the 2008 Australian Open.
He could sympathise with the Scotsman's frustrations, however, having been denied further Grand Slam glory for three years by the dominance of Roger Federer and Rafa Nadal.
"I think in my experience it was just a matter of belief, really mentally to mature and to understand what you need to do to become a Grand Slam champion and to become the best in the world," said Djokovic, who won three out of the four majors last year to clinch the world number one ranking before losing it to Federer after the Swiss's Wimbledon triumph in July.
"Andy has all the capacity he needs, all the talent on the court. He's dedicated, he's professional. He has proven that many years already with his results."
Djokovic said he savoured being part of the 'Big Four' of men's tennis, along with Federer, Nadal and Murray.
"Us four, we are taking this game to another level, and it's really nice to be part of such a strong men's tennis era," he added.
"It's a privilege to be part of this era. It's obvious that the four of us, you know, we get to the later stages of every single Grand Slam.
"Andy winning tonight makes it even more competitive and more interesting for people to watch it."