The crowds did their part to try to propel their fan-favourite Alcaraz past Medvedev, imploring the Wimbledon champion to keep fighting on Arthur Ashe Stadium.
But the Russian third seed simply overwhelmed his opponent, setting up a rematch of his successful 2021 finale against 23-time major winner Novak Djokovic, as he won 7-6(3), 6-1, 3-6, 6-3.
"These kind of matches can happen even if I feel myself (as a) different player, more mature," Alcaraz told reporters.
"I thought that, you know, right now I am better player to find solutions when the match is not going in the right direction for you. But, you know, after this match, you know, I gonna change my mind. I'm not mature enough to handle these kind of matches. So I have to learn about it."
Alcaraz rarely seems to let his frustration get the best of him on the court but admitted that he struggled to keep his temper on Friday, particularly as he was unable to come back in the second set.
But while the semi-final exit was undoubtedly a bitter end to an otherwise terrific North American hardcourt stretch, Alcaraz said he could keep the defeat in perspective.
"I don't think I'm gonna think about this loss for a long time. Of course I have to learn about it. I want to be better," he said.
"You know, these kind of matches help you a lot to be better and grow up in these kind of situations."
