British hearts were broken on the water as Fredrik Loof and Max Salminen triumphed ahead of the Team GB pair, who got silver.
The defending Olympic champions Iain Percy and Andrew Simpson sailed exceptionally throughout the week and came into today's medal race with an eight-point lead over Brazil's sailors.
But bronze pair Robert Scheidt and Bruno Prada did not prove their main challenge as the Swedes triumphed.
Great Britain needed fourth place or better in the medal race to guarantee them gold. They needed to finish sixth or higher should third-place Sweden win the medal race, which they did.
Britain entered the final leg of the race in sixth but slipped away in the last 100m to finish eighth, handing Loof and Salminen gold on the Nothe Course.