Edinburgh Diving Club’s Heatly and English athlete Birch were selected by Great Britain for the straight-to-final event that involved seven pairs on the opening day of the diving programme.
After the first round of dives they were sitting in third place on 91.00 points behind the Russians and the Ukrainians.
Heatly’s second dive, this one from the three metre board, was a good one earning 76.50 points, but Birch’s 10 metre effort only scored 45.00 and they slipped back to sixth after the second round.
They both put in good third dives, Heatly scoring 68.25 points and Birch, 24, 62.40.
That put them into second on 343.15 points at that stage behind Russia (349.55), but the Ukraine (355.90) then leapfrogged them to win gold and Germany (352.60) picked up the silver.
Heatly said: “We have not dived as a team a lot, but we are good friends and were excited to be paired together.
“It was a good experience and sets us up well for our individual events to come, but there were a few errors here and there and that really held us back from getting onto the podium.
“We will take some lessons away from this performance.”
Heatly, 21, now goes again on Tuesday in the men’s 1m event.