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In an error-strewn display, the 2012 bronze medallist needed 102 points from his closing dive to reach the final.
However, he managed only 50.40 to finish in last place with 403.25 - well short of the personal best of 571.85 he set in Friday's preliminary round.
"It's really hard to accept. I've worked so hard," said Daley, 22.
"Yesterday I scored the highest score ever in an Olympic Games. Today it wasn't meant to be. That's what diving does sometimes.
"I truly am heartbroken because I feel like I am in the peak physical condition and I could have won."
British Diving performance director Alexei Evangulov had said Daley was "in the best shape and best form of his career" before the Olympics.
Daley, who won a bronze medal in the 10m synchronised platform with Dan Goodfellow, suggested he would compete again in Tokyo in 2020.
"I'm so happy with how GB have done, so proud to be part of it and I wanted to be able to stand on top of that podium, so it will be another four years' hard work," he said.
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China's Chen Aisen, 20, claimed his second gold of the Games by winning the final, which took place later on Saturday.
Chen, who also won the 10m synchro alongside Lin Yue, scored 585.30 points to finish ahead of Mexico's German Sanchez (532.70) and defending champion David Boudia of the United States (525.25).
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Britain's Tom Daley said he was "heartbroken" after a shock semi-final elimination in the Olympic 10m platform diving competition.