The Empire State Building was an appropriate venue for Roger Federer to deliver his résumé of the US Open and if, as he said, the Swiss had slept for only 20 minutes on Monday night, his face and fascinating clarity of his thoughts, betrayed any lingering fatigue. Taller and taller he has become this past fortnight and there is plenty of room for further prosperity.

Andy Murray has developed, too. To reach the final of a grand-slam tournament at 21 has simply underlined what those with an appreciation of tennis accepted the first time they saw him play - that the Scot had only to grow into his body to become one of the best players in the world.

Listen to Federer, who won the final 6-2, 7-5, 6-2, discuss the litany of physical woes that he experienced as a younger man and it might make people appreciate Murray more. The holder of 13 grand-slam titles said: “I feel so much better physically than I ever have. Maybe this year was difficult, but today, the day after the final, I am like, ‘My God, I'm fresh, I'm feeling fine.' I played great towards the end of the tournament and don't have any of the niggling injuries I had when I was younger.

“When I was 20, 21, I used to have a sore arm every day. If I played a four-set match I'd have muscle pains everywhere, I couldn't handle anything over two hours. That doesn't happen any more - give me a four-hour practice and OK, I'm tired after it, but nothing is hurting. Even in 2005 [when he won two of the four grand-slam tournaments], I could hardly walk sometimes, my feet were hurting so much.” So what changed? “A lot of prevention work, better scheduling, being fitter, gaining more experience,” he said.

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Murray is not your polite public schoolboy. He’s a ferocious stand up and be counted Scot

Simon Barnes

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Which is exactly the point that Murray's career has reached. It has been a momentous few weeks for the British No1 and now he wants to go home, rest up, walk his dog and reflect. His time will come again.

He knows it and so does Federer. “You make the final of the US Open, it is a significant step,” the Swiss said. “It's not the quarters, the semis, it's the final. I started with a win in my first grand-slam final [Wimbledon 2003]; the motivation and inspiration drove me on. I am sure the same will happen with Andy. He will start to appreciate the game more and the effort the top guys have to put in to get so far. That will inspire him, I'm sure.”

As corks popped in the Federer section of the locker-room, Murray made a point of going over to congratulate each one of the victor's group. Many would have scurried for the exit.

On court, as they posed for pictures, the two talked animatedly. Murray smiled. One wondered what the conversation had been about. “He asked me if I got to keep the trophy,” Federer revealed. “I said that this is the one to win because you get a replica of the original size. Wimbledon is about 75 per cent, I don't know anything about the French and the Australian is small, so take the US Open and Wimbledon first because of the size of the trophies you get to keep. It was pretty funny.”

Federer did not want to say that winning the US Open had saved his season. “That doesn't sound right,” he said. “I just know I played excellent tennis towards the end and I felt invincible again for a change.”

Before he managed his 20 minutes of shut-eye, the champion went on to the internet to study images of his performance. “I wanted to get a sense of what the fans saw,” he said. “I like to see the pictures before I go to bed. I would never have done that at Wimbledon this year. I have never seen a picture of Rafa [Nadal] holding the trophy and it's something I don't ever want to see.

“I'm still a little bit disappointed a match like that was decided at night. I understand it was appropriate to finish it because of the special occasion we were under. Fair play, the crowds were there and they wanted a proper ending. But I think more people left feeling sorry for me than they were happy for Rafa, which hurts me a little. At the same time, I appreciate that tennis went up a notch with that match and that's what I strove to do in my five years as No1, to make tennis better, more popular and I admit that that Wimbledon final achieved all I had wanted, even if I lost it.”