Jack Draper has said that his spectacular breakthrough run to the semi-finals of the US Open has given him further belief that he remains on track towards competing for the biggest titles and claiming a place among the best players in the world – and possibly winning a grand slam title one day.

“I think even today I’m nowhere near what I’m capable of,” said Draper. “My tennis is improving but there’s still so much improvement in terms of my serve, my forehand, in many areas of my game. I’ve started to try and be more aggressive but I’ve still got so much room for improvement in so many areas and it’s extremely positive for me to know that I’m not anywhere near my potential and yet I’m still going to be a top-20 player in the world and making a grand slam semi-final.”

On Friday afternoon in New York, Draper was defeated by Jannik Sinner, the world No 1, in a dramatic match. After a tough opening set, Draper began to struggle physically in humid conditions, vomiting numerous times on the court, while Sinner fell during the second set and hurt his left wrist. Despite his struggles, Draper fought hard until the end.

The defeat ended the most important week in Draper’s career so far after he made his first deep run at a grand slam, which he achieved without dropping a set until his loss, and he will rise to No 20 in the world. Draper’s section of the draw had opened up following Carlos Alcaraz’s second-round loss to Botic van de Zandschulp and the 22-year-old took full advantage of the opportunity, piecing together five dominant performances en route to the semi-finals.

His loss was, in some ways, even more disappointing considering he was unable to produce his best level in the biggest match of his career. Yet Draper spoke with typically impressive perspective and openness after the match as he reflected on his journey to this point.

In addition to the humidity and the physicality of the rallies, Draper noted that his physical issues are related to the anxiety he sometimes feels before matches. While his desperation to win can be a massive asset, he admitted that he can sometimes want things too much. He continues to work on approaching his matches with more composure.

“I’m not patient because I’m a competitor, I want to keep on winning and doing all these things,” he said. “It is hard to reflect in tennis but at the same time, I am still very proud of the things I’m achieving since last year when I sat on the couch with a bad shoulder injury watching these guys in the semis of Wimbledon, winning Wimbledon, at the later stages of grand slams and getting to the top of the rankings. I was thinking: ‘Am I going to be able to do that?’”

It has taken a significant amount of work just for Draper to get to the point where he is physically able to compete week in, week out on the tour after so many injuries. He is adamant that he and his team are physically preparing him as well as they can and his issues on Friday are simply part of the process that will strengthen him in the long term.

“I think I’ve proved a lot to myself, especially in the last year, having stayed on court,” he said. “Obviously still working on a lot of things, but I stayed on court, stayed fit, improved my tennis and I am getting to the point where I am hoping to be one of those top players in the world very soon. I think, honestly, it’s just a matter of time because I can’t ask any more of myself. I’m doing all the right things.”

Draper can already look forward to the next challenges. Despite feeling slightly “beat up” in the aftermath of his defeat, Draper intends to represent Great Britain next week at the Davis Cup in Manchester.

“Davis Cup is a huge deal to me,” he said. “I never really understood it until I actually played it for the first time. I know the schedule in tennis is full and all these types of things. I remember when we were going to Colombia, it was a bit like: ‘Should I go, should I not?’ But I went and I saw how important it is to everyone, to be there representing your country. Even though the tennis schedule is relentless and honestly, I’ve barely had a day off since the start of the year. But I want to be there, I want to be competing, and I want to be playing for my country.”