The British pair started strongly, and led after three of the scheduled six dives.
However, a reverse three-and-half somersault during round four was sloppy and earned just 71.28 from the judges.
The dive dropped Daley and Waterfield to fourth in the standings, and despite two impressive final efforts, they could not climb back into the medal places.
Chinese duo Cao and Zhang, pre-event favourites, overcame a slow start and claimed the gold medal with a score of 486.78 overall.
Mexican duo Ivan Garcia Navarro and German Sanchez Sanchez took silver with some brave dives, including the most difficult dive of the event, rated at 4.1 on the scale, while American pair David Boudia and Nicholas McCrory won bronze.
“The crowd have been amazing,” said Daley afterwards. “I get emotional now just thinking about it. Fourth agonising after all the hard work.
“Our reverse 3.5 [the fourth dive] – you miss one dive like that and it’s over. It’s the way sport goes.”
“In this competition you can’t mistakes,” added Waterfield, “and we left ourselves with a lot to do – we finished with two brilliant dives but unfortunately it wasn’t enough.”
DALEY AND WATERFIELD – DIVE BY DIVE
Dive 1: Duo open with an inward dive with pike – and make a superb start
Difficulty 2.0 – score 56.4 – joint-1st with China
Dive 2: Reverse dive with pike – the same level of difficulty, and the same level of execution
Difficulty 2.0 – score 56.4 (total 112.8) – 1st, ahead of China by 0.6 points
Dive 3: Back 3.5 somersault in tuck position – rewarded by huge cheers, even from the watching David Cameron
Difficulty 3.3 – score 91.08 (total 203.88) – 1st, extending their lead over China to 2.4 points – Germany more than 12 points away in bronze
Dive 4: Reverse 3.5 somersault in tuck position – the moment it slips away. The synchronicity lets them down, and the execution bad. Both divers look frustrated as they slip back down the field.
Difficulty 3.3 – 71.28 (total 275.16) – 4th
Dive 5: Forward 4.5 somersaults with tuck – Daley’s entry into the water spoils an otherwise much-improved dive
Difficulty 3.7 – score 87.69 (total 362.85) – 6 points behind the bronze medal in 4th
Dive 6: Back 2.5 twists, 2.5 somersaults – the duo finish strongly with their highest-scoring effort of the competition
Difficulty 3.6 – score 91.8 (total 453.65) – Daley and Waterfield finish 4th, ending nine points away from the American pair in bronze.