The Serbian tennis legend ended his coaching relationship with his former rival last week after six months and felt that the experiment had run its course.
Djokovic said: "We felt like we couldn't get more out of that partnership on the court, and that's all there is to it.
"My respect towards Andy remains the same, even more actually, I got to know him as a person.
"I think he has a brilliant tennis IQ, he has a very rare mind of a champion that obviously has achieved what he has achieved, and he sees the game incredibly well."
Djokovic has taken a wildcard entry into the Geneva Open this week and explained that he will not be rushing to appoint a new coach following Murray's departure.
The world number six said: "At the moment, I'm not in need of a coach.
"I don't need to rush in any context. I feel comfortable with the people around me.
"In the next few tournaments, we'll see what happens."
Djokovic will make another attempt to win a record 25th Grand Slam title at the upcoming French Open and admits that he has found it hard to cope with a slump in form that has seen him fail to win a match on clay so far this season.
He said: "It's a different chapter of my life that I'm trying to navigate myself through.
"I'm not particularly used to having this kind of circumstances where I would lose a consecutive match, tournaments, first rounds and so forth. I don't think it ever happened for me in the last 20 years. But I knew that eventually that moment will come.
"I'm trying to do well, I'm trying to win more trophies, I'm trying to build my form for Roland Garros, and perform at the desired, necessary level in order to go far in the tournament and challenge the best players in the world.
"So yes, the motivation is still there."