A tearful Novak Djokovic lost the US Open final and the chance for a calendar sweep of the majors but said the love he felt from the crowd meant "as much as winning 21 Grand Slams".

The world number one, who has never garnered the same support from the stands as his big rivals Roger Federer and Rafael Nadal, was brought to tears by the Arthur Ashe Stadium's raucous reaction towards the end of the third set.

Having broken Medvedev's serve and then holding for 5-4, there was a huge roar at the changeover as the Serb regained a glimmer of hope after being 5-2 down.

And while Djokovic failed to surpass the Grand Slam title tallies of Federer and Nadal - the trio remaining locked on 20 majors each - he said the warmth he felt made him as happy as if he had.

"Even though I have not won the match, my heart is filled with joy and I am the happiest man alive because you guys made me feel very special on the court," he said in an emotional on-court interview.

"You guys touched my soul."

The New York support has not been the kindest to three-time champion Djokovic in the past, particularly when he has faced Federer, like for instance in the 2015 final won by the Serb.

That has been the case at other major venues, where he has not enjoyed the adoration heaped, for example, on Federer at Wimbledon or Nadal at Roland Garros, often cast as villain rather than hero.

However, the majority of the 23,000 fans inside the Arthur Ashe Stadium were behind him from the first shot in his ultimately unsuccessful bid to make history against Russia's Medvedev.

Djokovic added: "Of course, part of me is very sad. It's a tough one to swallow, this loss, I mean, considering everything that was on the line.

"But on the other hand I felt something I never felt in my life here in New York. The amount of support and energy and love I got from the crowd was something I'll remember forever.

"The emotion, the energy was so strong. I mean, it's as strong as winning 21 Grand Slams. That's how I felt, honestly. I felt very, very special. These are the kind of moments that you cherish."

Not since Rod Laver won all four Grand Slams in 1969 has a male player achieved the feat and Djokovic, now 34, may consider this was his best, and perhaps last, chance to match the Australian.

Afterwards, Djokovic admitted to feeling "relief" that his quest for the calendar Slam, a target that gathered more and more steam as the year progressed, was over.

"The build-up for this tournament, everything mentally, emotionally I had to deal with throughout the tournament in the last couple of weeks was just a lot," he said.

"It was a lot to handle. I was just glad that finally the run is over. At the same time I felt sadness, disappointment, and also gratitude for the crowd and for that special moment they created."

Former British number one Laura Robson, commentating on the final as a pundit for BBC Radio 5 Live, felt Djokovic paid the price for the exertions of a long year in which he also reached the semi-finals at the Olympics.

"We are so used to him winning these Grand Slam finals over and over again but he just had nothing left in the tank, nothing left to give," Robson said.

"There was that lovely moment towards the end when the crowd supported him like that and gave him all the credit that he's been asking for.

"There was so much pressure on him - we think he's superhuman and we expect him to make history time and time again but it just goes to show that it is so, so tough out there."