The Scot became the first British man in 76 years to win a major singles title when he beat Novak Djokovic over five sets in the US Open final.
The success completed a fine few months for the 25-year-old, who followed reaching the Wimbledon final with winning Olympic gold.
It also came hours after Britain's Olympic and Paralympic athletes were saluted with a parade around the streets of London, attended by hundreds of thousands of people.
Murray hailed the effect Britain's magical sporting summer has had on the country, saying: "Being around the Olympics and seeing how the nation came together, from the public to the athletes to the press, everyone was just right behind it.
"I saw some of the pictures of the parade and it's just amazing to see how pumped everyone was. It's been amazing to be part of it.
"Sport has been this huge part of my life since I was a kid and it's been the best summer of sport in my lifetime and I'm sure in most people's. It's been so much fun and I'm just happy I was able to contribute towards it."
Murray is hoping to be able to take part in a similar parade for Scotland's athletes in Glasgow on Friday.
His biggest worry about winning a grand slam was how much his life would change, and he laughed off talk of a knighthood as "a bit rash".
The Scot's odds of becoming BBC Sports Personality of the Year have been slashed, but he is not expecting to be made Sir Andy Murray any time soon.
He added: "A lot of my friends have been messaging me about it and I don't really know what to say. I think it should take more than one or two good tournaments to deserve something like that. It would probably be a bit rash."
The final finished after 2am British time but many people in Murray's home town of Dunblane and across the country stayed up to watch and celebrate the Scot's success.
He received messages of congratulations from Prime Minister David Cameron among others, and he admits the reaction he will get when he arrives home is something he cannot yet imagine.
Murray said: "All of that will probably hit me when I go back. It's something that will probably take a bit of getting used to. It's not something I've always been that comfortable with.
"I spoke to (coach) Ivan (Lendl) a couple of times during the year and he asked me, 'What worries you?'.
"And I said that I worry what might happen if I win a major, how my life might change, because I want it to be the same.
"He said he felt the same thing but all that happens is you get more people congratulating you and you get nicer tables in restaurants and to play on all the good golf courses for free."