"Sorry to the fans and to Novak, because we all know what he was going for," Medvedev told ESPN at the trophy presentation.
"With what he accomplished this year and for his career, I've never said this to anybody, but he is the greatest tennis player in history."
Djokovic, ranked No. 1, entered the match with a chance to become the first man since Rod Laver in 1969 to capture a calendar-year Slam. Steffi Graf was the last player to accomplish the feat , in 1988. Djokovic held back tears as he accepted his runner-up trophy amid cheers from fans.
An exhausted but joyful Medvedev sprawled briefly on the court after Djokovic hit his final return into the net, resulting in championship point for the 25-year-old. The No. 2 player in the world claimed a $2.5 million first-place prize.
Medvedev fired 16 aces, 38 winners and converged four of eight break points in the two-hour, 15-minute match. Djokovic totaled six aces, converted one of six break points and logged 38 unforced errors.
Djokovic struggled to keep his composure throughout the match. At one point in the second set, out of anger, he slammed his racket down three times, twisting it out of shape.
"It was an amazing match and an amazing tournament," Djokovic said. "If there is anyone that deserves a grand slam title its him. Well done."
Medvedev broke Djokovic's first serve in the first game. He also claimed the second game, but Djokovic rallied to get the set to 5-4 with a win in the ninth game. Medvedev closed out the set with consecutive game points.
Djokovic won two of the first three games in the second set. Medvedev won the fourth game and broke Djokovic's serve in the fifth game.
He pushed his advantage to 4-2 with another triumph in the sixth game. Djokovic tightened the second set to 5-4 with another win in the ninth game. Medvedev then won the set on a Djokovic backhand return error.
Medvedev broke Djokovic in two of the first three games of the third set. He pushed his advantage to 4-0 in the set with another victory in the fourth set. Djokovic broke Medvedev's serve and fended off championship point in the eighth game.
He tightened the set to 5-4 when he won the ninth game on an errant Medvedev return. Djokovic attempted to return a Medvedev serve on a final backhand swipe, but the effort couldn't clear the net.
Djokovic started his quest for a calendar Slam in February, beating Medvedev in the Australian Open final He added a clay-court crown in June at the French Open. He won his third Grand Slam of 2021 in July on the grass courts of Wimbledon.
"I was thinking of both scenarios [a win or loss] and visualizing what I would say," Djokovic said.
"I would like to say that tonight, even through I have not won the match, my heart is filled with joy and I'm the happiest man alive because [the fans] made me feel very special on the court. You touched my soul."