Djokovic, who was looking to become the first man in the Open Era to win all four Grand Slams twice, lost 0-6, 2-6, 5-7 to Nadal on Sunday.
"What you are doing in this court is unbelievable. Throughout your career you have been a great champion," said Djokovic.
"Today you showed why you're king of the clay. I have experienced it on my own skin. It was a very tough match for me today, obviously I'm not so pleased with the way I played but I was definitely overplayed by a better player today on the court."
Djokovic also congratulated the organisers for successfully holding the tournament. Originally scheduled to be held from May 25 to June 7, the 2020 French Open had to be postponed to its eventual dates of September 27 to October 11 due to the Covid-19 pandemic.
"It has been a fantastic four weeks. The situation is very difficult for everyone and we were all worried whether we can play the sport we love. So thank you to all the organisers for making this possible," said Djokovic.