The duo, who will represent Team England at next month's Commonwealth Games in Australia, had been on course for a silver medal at the National Aquatics Centre but dropped to third courtesy of a disappointing final dive of the day.
As expected, China's Chen Aisen and Yang Hao took gold thanks to a flawless routine, eventually finishing more than 65 points ahead of the chasing pack.
Daley will now go on to compete in the mixed 3m synchro with Grace Reid tomorrow, before performing as an individual in the 10m platform on Sunday.
Men's 10m synchro results in full:
1. Chen Asien, Yang Hao (CHN) - 484.29
2. Oleksandr Gorshkovozov, Maksym Dolgov (UKR) - 417.93
3. Tom Daley, Daniel Goodfellow (GBR) - 400.68
4. Kim Yeongnam, Woo Haram (KOR) - 393.63
5. Aleksandr Bondar, Viktor Minibaev (RUS) - 385.86
6. Florian Fandler, Timo Barthel (GER) - 371.82