Djokovic hurled one racket into the stands and smashed another in a 6-4 6-7 (6) 6-3 derrota.
The world number one was back on court less than 24 hours after his shock defeat by Alexander Zverev which ended his hopes of becoming the first man to complete the Golden Slam of all four major titles and Olympic singles gold in the same year.
Djokovic’s dejection was clear afterwards, especially when he then lost his mixed doubles semi-final with Nina Stojanovic, and rousing himself to finish on the podium proved beyond him.
He saved a match point in the second set to force a decider but let his emotions out early in the third when he failed to break, hurling one racket into the empty stands and then smashing another against the net post, as he fell to a 6-4 6-7 (6) 6-3 derrota.
This was the third time Djokovic has played a bronze medal match at the Olympics. He defeated James Blake in Beijing in 2008 but lost to Juan Martin Del Potro in London.
He had made winning a medal for Serbia one of his major goals for the season but his serve, which had gone badly off the boil against Zverev, was missing in action again in the first set and Carreno Busta broke for 3-2 while saving all five break points he faced.
He held his own in the second set, his serve much improved, but Carreno Busta repelled everything Djokovic could throw at him and he came from 1-4 down in the tie-break to force a match point at 5-6.
Djokovic showed his heart was still willing by saving it and taking the contest to a decider but things quickly took another downward turn.
Carreno Busta was the opponent at the US Open last summer when Djokovic was defaulted for hitting a line judge with a ball and, when the Spaniard saved a break point in the opening game, his opponent again had a worrying loss of control, flinging his racket into the stands.
Remarkably, he did not receive a warning, and Carreno Busta was clearly shocked that Djokovic was not given a point penalty when he angrily destroyed another racket after falling 3-0 atrás.
He tried to turn the match around but Carreno Busta, who has played the best tennis of his career over the last year, withstood superbly to claim his first Olympic medal, finally clinching his sixth match point.
The 30-year-old lay amid the Olympic rings at the back of the court in celebration as his opponent waited to congratulate him at the net.
After his singles defeat Djokovic revealed he had pulled out of his mixed doubles bronze medal match, where he and Stojanovic had been due to take on Australia’s Ashleigh Barty and John Peers in a rare meeting of the men’s and women’s world number ones.