Stan Wawrinka beat the best when it mattered, yet the quietly spoken Swiss with a hint of devil in his eye is reluctant to climb up on the podium alongside the vanquished Novak Djokovic and the trio who constitute the Big Four of tennis.

He has beaten them all at some stage – his absent compatriot Roger Federer, Andy Murray, Rafael Nadal and, in two of his major finals, the best player in the world. So his victory over Djokovic to win the US Open in four sets of extraordinary passion and anxiety – his third major – , with just Wimbledon to conquer – surely gains him entry to this elite club.

He will not have it. His voice croaking a little from a solid night’s celebrating in New York, one of his favourite cities, he explained why in a spectacular setting at the top of the Rockerfeller Center in Manhattan on Monday morning. “Because first I think it’s not fair for them to put me there,” he said. “They have been there since more than 10 years. They have been in all semi-finals of grand slams, all finals, all semi-finals of Masters 1000, all finals.

“They have been winning everything and I think it is just not fair. The big four stay the big four, like that. I am me. I have been achieving something that I never expect the last three years, I have been winning three grand slams and it’s more than amazing. But I don’t want to keep talking about being part of them or close to them. The big four stay the big four. It’s part of tennis history, and it will always be like that and I think it’s great like that.”

Such self-effacement is touching. It also makes the world No3 and triple-slam champion dangerous among his peers because they never know quite what to expect. A close friend of the player said there was a feeling around his camp before the tournament, and especially before the final, that this could be Wawrinka’s Open.

He agreed. “When I arrived before the tournament I knew I was ready, I knew I was playing really well, moving the best I have ever moved before on a tennis court. I was practising great. Then I checked the draw and saw my first match it was Fernando Verdasco and I knew I had to be ready. When the tournament starts I don’t think about whether I’m ready to win or not. I just think about match after match.

“Yesterday was the same in the final against Novak. I told Magnus [Norman, his coach] before the match I had a feeling, but this time I have even more confidence to beat him. I feel better than him. It was the first time ever I had this feeling in a tournament and in a match.Maybe that’s also one of the reasons I played so well again.”

Nor was he keen to criticise Djokovic for what many regarded as blatant gamesmanship when he took two medical time outs for repairs to his feet after being broken in the fourth set, although Wawrinka admitted he was confused by the timing of it. “I think some times some players abuse the rules, for sure,” he said. “But I think also you need to understand that sometimes you have real pain but you try to push, to push. You play a few points and then you stop.

“Yesterday I don’t know exactly what happened but the second they told me – because normally you have only one – they told me it was because he was bleeding. For me it’s normal the guy is bleeding and you have to do something and I have no problem with that.

“Sometimes I feel also from outside no one tells people what’s happening. When he took the second one they come to me and they say, ‘I’m sorry, we have to take three minutes because he is bleeding and we don’t want to leave it like that’ and I have no problem with that – but people outside or behind, they cannot see.”

What they did see was a gracious and humble champion getting the result he deserves. He might never win Wimbledon to complete a set of all four majors but he has already done enough to be considered alongside the best of his generation – whatever he thinks to the contrary.