Draper has burst into the spotlight at Flushing Meadows, beating Alex de Minaur to become the first British man to reach the semi-finals of the US Open since Andy Murray in 2012.
The 22-year-old, who had never previously made it past the fourth round of a Grand Slam, has won just one title on the ATP Tour and spent much of 2023 sidelined by a shoulder injury.
"Last year was a real turning point for me, when I had my injury setbacks and took a lot of time off over the summer because of my shoulder injury," Draper told reporters.
"I had to watch all these young, amazing players winning amazing tournaments. I was playing on the biggest stage in the world and I felt like I just wasn't doing enough to get to that point myself.
"This is not an overnight thing for me. I've believed for a long time that I've been putting in the work and doing the right things. I knew that my time would come."
Draper has won all five of his matches at the US Open without dropping a set, but he said he was confident in his ability to be competitive over five sets.
"I've been feeling like a more complete player. Physically I've always worried a little bit about playing five sets and mentally and emotionally it being too much for me," Draper added.
"I still feel like I have got so much left in my locker. It gives me a lot of peace of mind knowing that my body feels good or robust, and I'm ready to go the distance if I need to."
In the semi-finals, Draper faces either Australian Open champion Jannik Sinner or 2021 US Open winner Daniil Medvedev, who meet later on Wednesday.
The Briton has played both of his potential opponents once before, beating world number one Sinner on grass in 2021 and losing to Russian Medvedev in the Italian Open earlier this year.
Asked if those experiences would help, Draper said: "I think it helps being on court with both of them. When I played Daniil in Rome, I didn't know what to expect...
"It is tough when you play the best players in the world, you don't know what to expect and you watch these guys winning Grand Slams on TV.
"You think, 'I'm going to go out there tomorrow and they're going to be way too good for me'. Whereas if you put your game on the court and if you do the right things, you do get chances here and there."
