Playing with a new-found self-belief, Murray surged into the final at Flushing Meadows and managed to hold off everything defending champion Djokovic threw at him to triumph in four hours and 54 minutes.
"I want to keep improving," said Murray. "I know how it feels to win a Grand Slam and winning the Olympics.
"I think I'll get a better feel when I get back on the court and start practising again, I'll feel what it's like to have a bit more belief in myself and my shots.
"I could have won Wimbledon this year, I was very close. I know if I'm in that position again, I'll take the same chances, I'll go for my shots again.
"A little bit more confidence and experience of taking my chances in big matches will help me."
Murray has been a busy man since breaking his major duck shortly after 21:00 New York time.
He celebrated with a team dinner, where he stuck to being teetotal, before appearing on the CBS breakfast show on Tuesday morning.
He then headed to a photoshoot in Central Park and a reception at British Consul Danny Lopez's official residence in Manhattan, where he was welcomed by Scottish piper Don Neil MacRitchie playing Scotland The Brave and presented with a hamper of British food and drink.
The moment Murray won the US Open
"I wasn't able to sleep last night," said Murray. "I wasn't bouncing off the walls or anything, I just couldn't go to sleep, I was just sitting awake for a few hours.
"During the tournament, if I'd had an hour and a half's sleep and had to get up I would have been in the worst mood ever but I woke up and jumped out of bed at 6.30am, which isn't like me. I'm very excited but it'll probably take a few days for it to sink in.
"It's something that will probably take a bit of getting used to. [Attention] is 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, you get nicer tables in restaurants and to play on all the good golf courses for free."
Murray will now turn his attention to the ATP World Tour Finals in London in November and a tilt at the world number one spot next year.
"All players, once you get near to the top of the game, one of the goals is to try to get to world number one," he said.
"I can't say this year it's necessarily possible for me to do it because I didn't have a particularly good clay-court season and I didn't do well in the Masters Series in Cincinnati and Montreal and also in Indian Wells.
"But that is the next step. To do that, you need to be consistent throughout the whole year. That's something that Novak and Roger and Rafa [Nadal] have done incredibly well the last few years.
"I'm definitely going to try. It's something I'd love to do, to get to number one. It's a very tough thing to do."
Asked about the prospect of a knighthood, Murray said: "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."
Meanwhile, Murray's coach Ivan Lendl believes the Scot can go on to even greater success.
Lendl, who became Murray's coach at the start of 2012, said: "Hopefully, we're not anywhere near where Andy can get.
"He won two big ones in this fantastic year. I'm very happy for Andy. It's a great achievement and let's hope he can continue and rake up more.
"Andy has been maturing very nicely as a player, as a competitor, as a person. As you mature you become more comfortable in these situations.
"Of course, it's very important to be in more of these situations and the more of them you are in the more comfortable you feel."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.