The Australian crew of Olivia Price, Nina Curtis and Lucinda Whitty have lost only once in 15 races in the head-to-head match racing event spread over both weeks of the Olympic regatta.
Finland won their quarter-final 3-1 against training partners the United States who were competing in Olympic gold medallist Anna Tunnicliffe's boat.
Tunnicliffe, the British-born former Laser Radial champion said: "Yes it's heartbreaking. It's been a phenomenal series. We're bummed but we'll cheer for the Finnish for the gold now.
"We've trained together so we all know each other really well. Our next goal is to get fifth in the playoff."
Finland skipper Silja Lehtinen said: "We're really happy with our sailing but we're heartbroken for them".
Spain's Tamara Echegoyen Dominguez and her crew of Sofia Toro Prieto Puga and Angela Pumariega Menendez won their last eight clash against the French 3-0 and will now face Russia.
Echegoyen Dominguez said of their racing: "We were more aggressive in the downwind and that is good for us... now we will have to work hard again in the semi-finals".
Russia's 3-2 win over Britain survived a protest by the British with the Russian skipper saying they had won fairly.
"I think we won on the water. It was really close but the race committee know their job. I think you have to win on the water, not on the shore," said Ekaterina Skudina before a jury decision later turned down Britain's protest.
"Five races, really close. I think we made a lot of mistakes because we were quite stressed. But still we could manage it, " she added.