The 20-year-old 15th seed was outwitted by the unseeded Medvedev in a series of long, intense rallies in blistering conditions on an outside court at Flushing Meadows.
Tsitsipas said he had found it hard to recover from another punishing match on Monday against experienced Spaniard Tommy Robredo.
"I had no energy. But I managed somehow, you know, rehabilitate and get ready for the second-round match," Tsitsipas told reporters. "But it didn't feel the same."
He struggled in the humid weather as temperatures climbed above 90 degrees Fahrenheit (30 degrees Celsius).
"You breathe this heat that's coming, the moisture that's in the air. So you feel like you're empty," Tsitsipas said. "You're not breathing out, breathing in, breathing out, so it feels really awkward to be playing like this."
The in-form Tsitsipas reached the Rogers Cup final this month before losing to world number one Rafael Nadal and his recent performances have earned plenty of plaudits.
Former player Brad Gilbert, who coached Andre Agassi, last week described Tsitsipas as "unbelievably athletic" while five-time U.S. Open champion Roger Federer said he believes the Greek is among the next generation of players poised for a major breakthrough. [nL2N1VD0MN][nL3N1VF5BK]
(Reporting by Amy Tennery, editing by Ed Osmond)
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