Kyrgios' 7-6(11) 3-6 6-3 6-2 win meant the 26-year-old Medvedev will lose the bulk of the 2 000 ranking points he claimed by lifting his maiden Grand Slam title at Flushing Meadows last year.
"I'm trying to look good here, but I'm disappointed," Medvedev told reporters.
"Not going to cry in the room, but I'm a little bit disappointed. For a few days, I'm going to be just a little bit sad, looking at my phone, my laptop or watching some series."
Spaniard Rafael Nadal ranked third, is in pole position to reclaim the top spot when the rankings are updated next Monday as he is defending no points and playing the hardcourt major for the first time since 2019.
Fourth-ranked Carlos Alcaraz and Norway's world No 7 Casper Ruud also have a shot at the top spot.
"It was not the first thing on my mind walking after the match, saying, 'Damn, will not be the world No 1 anymore'," Medvedev said, adding that losing the top spot would motivate him.
"I actually don't know which place I will be. Probably three, four. I guess Carlos will pass me. I don't know actually."
After losing to Nadal in the Australian Open final at the start of the year, Medvedev exited the French Open in the fourth round. A ban on Russian players at Wimbledon due to Moscow's invasion of Ukraine forced Medvedev to miss the grasscourt major.
"Obviously, it was the last slam of the year. Didn't do well enough. Didn't win in Australia when I had the chance. Didn't get the chance to play at Wimbledon. Roland Garros lost the fourth round. Here fourth round," he said.
"Yeah, should do better. Should get more points if I want to be world No 1 again."