The Briton suffered his eighth reverse in 10 major finals, with five of those defeats inflicted by Djokovic, and was reluctant to reflect on the achievement of reaching his first Roland Garros final.
Murray started promisingly by taking the first set in Paris, but the 29-year-old had few answers as Djokovic proceeded to move through the gears on Philippe Chatrier court.
The world number one became just the third player after Don Budge in 1938 and Rod Laver, in 1962 and 1969, to simultaneously hold all four Grand Slam trophies.
"It's such a rare thing to have happened, and obviously the depth in the game just now is strong. Some people may think differently, but the level of tennis I think is pretty high now and something you probably won't see for a long, long time," said Murray.
"His performances over the last 18 months to two years have been exceptional and he deserves to be number one."
The Serb also joined contemporaries Roger Federer and Rafael Nadal in an exclusive eight-man club of players to have completed a career Grand Slam. Murray, the 2012 US Open and 2013 Wimbledon champion, admitted he was disappointed to lag behind Federer, Nadal and Djokovic but remained confident of adding to his two major titles.
"Obviously the guys I have been around the last few years have made things difficult for me. I have been close-ish to winning all of the Slams now and unfortunately all of them have done it instead.
"But I guess I've got a few more years to try and do that. I think when I finish I will be more proud of my achievements maybe.
"None of the big events I have won have I done it without beating one of those guys or a couple of them. So, yeah. Maybe when I finish playing, my achievements will mean a little bit more."
Djokovic's victory in Paris improved his record against Murray to 24-10, but the Briton vowed to come back stronger and avenge Sunday's pain should the pair meet at Wimbledon next month.
"I'm very disappointed. You know, from 13 days ago, I maybe would have signed to have been in this position. I was struggling. I was a couple of points from going out of the tournament in the first round. But then when you get there obviously you want to win."
Murray will switch his focus to acclimatising to grass next ahead of the pre-Wimbledon tournament at Queen's which starts June 13 and is again set to feature 15 of the world's top 30 players.
Second-ranked Murray is bidding for a record fifth title at the west London venue having lifted the trophy in 2009, 2011, 2013 and 2015.
"I have played some of my best tennis on clay, for sure, over the last few weeks and definitely last couple of years," he said.
"Hopefully that translates well onto the grass, which is a surface that comes way, way more natural to me.
"So, yeah, I will try and have a good run on the grass. You know, if we meet on the grass, I'll try and learn from the last few weeks' matches and see things I could have done better."