Medvedev was deposed as US Open champion on Sunday by Kyrgios as the fiery Australian stormed to an electrifying 7-6 (13/11), 3-6, 6-3, 6-2 win to reach his first quarter-final in New York.
"Nick today played kind of at the level of Novak and Rafa," said the 26-year-old Medvedev after seeing 21 aces and 53 winners speed past him.
"He has a little bit different game because he's not a grinder. At the same time he can rally. He's tough to play. He has an amazing serve.
"But from baseline it's not like when the point starts, you know that you have the advantage. He plays good. He has every shot.
"If he plays like this until the end of the tournament, he has all the chances to win it."
Medvedev, who will lose his world number one ranking following his defeat, was attempting to become the first man to defend the US Open title since Roger Federer in 2008.
Instead, he ends the Grand Slam year with a runners-up spot at the Australian Open, where he was defeated by Nadal, and last-16 exits at the French and US Opens.
Along with other Russians, he was banned from Wimbledon due to the invasion of Ukraine.
Medvedev said his physical condition began to deteriorate as the match went on, a legacy of picking up a fever during the tournament.
"In the USA, I get sick for sure in the hardcourt swing because the AC is just crazy," he said.
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