Before this year, the furthest Murray had gone in a grand slam was the fourth round. At Wimbledon this summer he went a round further, reaching the last eight before losing to Rafael Nadal. It seemed possible then that he would have to undergo another couple of losses in quarter-finals before finding it in him to force his way into the last four, but the US Open has revealed such gradualist thinking to be unduly pessimistic.

Never mind racking up another couple of losing quarters before taking just one extra step. This time Murray battled all the way through to the final, in the process defeating Nadal for the first time.

In the new ATP rankings released yesterday, Murray is up to a career-high No 4. He is still some way behind Federer, Nadal and world No 3 Novak Djokovic, but he is definitely the best of the rest now. Nadal has reached incredible heights this year and Federer was back to his brilliant best on Monday night – one of yesterday's headlines summed that up rather well by proclaiming "Roger Federer becomes Roger Federer again" – but Djokovic has not kept pace. The Serbian, a week younger than Murray, has a big advantage in the rankings at present, but the Scot can be expected to eat into that in what is left of this season before mounting a real challenge for the No 3 spot next spring.

So Murray has undoubtedly made substantial progress. He is no longer a mere member of the peloton chasing the big three, but has struck out on his own now. His next step will be to go from best of the rest to junior member of a dominant quartet.

He knows there are aspects of his tennis he needs to work on, but he has now shown that he has an excellent all-round game and few serious weaknesses. And, for all that Federer's grace and Nadal's almost absurd energy levels can leave spectators gasping, it is perhaps Murray – along with Richard Gasquet – who has the most aesthetically pleasing play. And the Scot is a lot tougher mentally than the Frenchman, as he showed during their epic battle at Wimbledon.

Still, try as he might, Murray was unable to get any more than a toehold in the final. It was his misfortune to come up against Federer at a time when the deposed No 1 was possessed with an ardent desire to prove himself anew, to confound those who said he was finished at the age of 27.

For Federer was not simply playing against Murray on Monday night. He was playing against the memories of losing in Australia to Djokovic, of being humiliated by Nadal at Roland Garros, and of having his Wimbledon crown then his No 1 ranking usurped by the Spaniard. He was playing, if not to erase those memories, at least to lessen their significance. He was playing to prove that none of them marked the beginning of the end for him.

The ruthlessness with which Federer went about trying to make his point was evident from the first game, in which Murray came close to looking like an ant which gets in the way of a tank. Indeed, for the whole of the first set, which lasted all of 27 minutes, Federer was unstoppable.

The second set was far more even, and Murray was still in it at 5-5, but when it mattered Federer raised his game again and took it on his opponent's serve. The third was close to being a rerun of the first.

Federer did have one obvious advantage, in that he had had a proper rest after winning his semi against Djokovic, while Murray was playing for the third day in succession. True, the resumed match against Nadal only lasted a set and a half and cannot in itself have taken too much out of him, but the preparation time and the waiting around can take their toll too.

Yet those are the vagaries of tournament play, and Nadal for his part might have argued that his exertions in winning the Olympic title had rendered him susceptible to defeat by opponents who, like both US Open finalists, had been eliminated early on in Beijing and thus had more time to reacclimatise in the west. No competition can ever be scheduled completely evenly for all players: sometimes the breaks go for you, sometimes against, and the better you are as a player, the more you are able to negate any minor disadvantages.

In any event, although a rested Murray may have pushed Federer a little harder, the Swiss player would surely have still been too good for him. And for Murray, the issue is not just one of physical rest, but of recovering mentally from prior exertions.

It is notable that most of his really big wins have been followed by lacklustre performances. Losing to Marcos Baghdatis at Wimbledon 2006 after beating a stunned Andy Roddick; going down to Nadal at the same venue this year after coming back to beat Gasquet in five; and now losing to Federer after beating Nadal for the first time, in his first Grand Slam semi-final. Whether the root cause is physical or mental, there is a pattern here which needs to be examined.

But Murray will do that. In fact, he will continue to examine every aspect of his game, ironing out imperfections, fine-tuning his technique. And he will continue to get better. And he will, in the not too distant future, win his first grand slam.