After a lopsided first set where everything was working in Djokovic's favour, Medvedev had an excellent chance to level the match in the second but squandered a set point at 6-5.
"Regrets, for sure," he told reporters after the match.
"(The) second set was the best set I played and I didn't win it.
"So that's why I kind of, I would say, it's normal that the match went that way, because first and third he was kind of better and not much to say. Second, if I would win it, (it) maybe could have been a different game."
Medvedev endured a bumpy run-up to the year's final major, withdrawing from Washington with an injury and going out in the third round in Cincinnati, and there was little to suggest he could repeat his successful 2021 campaign at the US Slam.
But he found his rhythm in New York, battling through the draw before digging deep to send top seed Carlos Alcaraz packing in the semi-finals.
The Russian told reporters on Sunday he had not felt in peak condition since a four-set grind against Alex de Minaur in the fourth round.
"Sometimes in a Grand Slam you're not going to feel 100% and you may still win the whole thing," said Medvedev, who picked up two Masters 1000 titles in 2023.
"For sure physically I would like to come better to this match, but if you play Carlos in the semi-finals, you know that physically it's going to be a tough one.
"So there is no other choice and you still want to win and just I had to be better physically, mentally, and tennis-wise."
