Heslop and GB diving partner Oliver Crompton finished fourth in the final – less than four points off a medal.
They were in second spot after their first two dives but dropped out of the medal placing with their next two efforts.
It did look like they were going to steal a medal in the last round with a 65.28 point score to move into third with just one pair to go, but the Belarus pair of Molchan and Saurytski, who dived last, overtook them and the Germans to take silver. Gold was won by Russians Ivanov and Trenovoi.
Heslop will be looking for individual success on Sunday when he competes in the boys’ A platform competition.
Meanwhile, there was more joy for Plymouth Diving at the Swim England National Age Group Championships in Sheffield.
Maria Marasescu, competing as a guest, won the girls’ 16-18 platform competition with 245.60 points.
There was a second silver medal for Oliver Heath in the boys’ 9-11 category. Having finished second behind his team-mate Theo Stevens in the three-metre competition, he then claimed the same colour in the platform event.
Heath was leading going into the final round but he was overtaken by Luton’s Jorden Fisher-Eames.
There was also a silver medal for Scarlett Colbourne in the 9-11 year-old girls’ three-metre event.
The Plymouth diver was just beaten for the title by Crystal Palace’s Corin Burrows-Mackley.