Draper said afterwards he was not angry with Medvedev and did not blame him.
“First of all, Daniil was the stronger player fair and square,” the 24-year-old told BBC Sport.
“It’s a difficult situation for the ref. I don’t think I did enough to hinder him, but at the end of the day I did make a slight thing with my hands.
“On one hand, I get it, but on the other, I don’t think it was enough to distract Daniil.
“If he had missed the next ball and it was very clear that I had hindered him, then I would get it.
“I think he’s played the rules quite well. The rally carried on and I was able to win the point so I don’t think I should have lost the point. I think it’s pretty harsh.”
Medvedev, who goes on to play Carlos Alcaraz in the semi-finals, said he did not feel “good” about the incident but denied he had cheated.
“Was I distracted big time? No,” the world number 11 said.
“Was I distracted a bit? Yes. Is it enough to win the point? I don’t know.
“If you look on the first forehand I do after it happened, I think I could have done a better shot if there was no gesture from Jack.
“Do I feel good about it? Not really, but I also don’t feel like I cheated. I let the referee decide.”
