Djokovic was unconvincing as he progressed to the last 16 over four sets in a match which required two tie-breaks.
The pair were on court for four hours and there was little to separate them until Djokovic cranked through the gears to take the final set 6-2.
The Serbian embraced his opponent at the net after the battle and Bautista Agut has lifted the lid on what was said.
“Yeah, kind words we have at the end of the match,” Bautista Agut said.
“It’s a pleasure for me to play against Novak always.
“And we played some really nice matches and, unlucky for me, I lost more than I won.
“But it’s nice to play against him.”
The pivotal moment in the game came when Djokovic won the third-set tie break to take a 2-1 advantage into the fourth.
And Bautista Agut explained that losing that set was fundamental in the defeat.
“Well, I was very focused on the match, and I think I played great and I was at the same level as Novak,” he added.
“And I had my chance in the third set, and, well, I couldn’t make it.
“And when you play against a great champion, you don’t have many opportunities.
“Well, he is a great champion. He is one of the best tennis players in the history.
“And, of course, if he keeps pushing like this and fighting, as always he did, he will be on the top again.”