Victory was needed to advance to a semi-final bout with Sweden on Thursday evening, and Kyle Smith's rink began well, only for the Swiss to claim the ninth end 5-0 and take an unassailable advantage.
"We gave it our best shot but that's the dream over," the British skip said.
"We started off very strong and we put ourselves in a great position and a couple of missed shots were the difference in the game.
"They are a good aggressive team and when they make a lot of shots it is hard to defend against.
"It's a sore one, we gave ourselves the chance of making the semi-finals but we couldn't make it happen."
Britain had chances in the contest against a team they had beaten in the round-robin phase.
Kyle Smith's perfectly-weighted final stone on the eighth end gave Britain a 5-4 advantage with two ends remaining.
But Switzerland scored a remarkable five in the ninth end as skip Benoit Schwarz sent his final stone through two guards to dislodge another British stone for an astonishing turnaround.
British men's coach Viktor Kjell said: "We are very disappointed and I thought we were the better the team the whole game but they stepped it up.
"I just don't know what happened in that ninth end. We missed four or five shots in a row and you cannot afford to do that at this level.
"I thought we'd almost got away with it and then he plays a pistol shot and walks away with a five."
Kyle Smith added: "I'll take a lot from the experience coming to the Olympic Games with my best friends and my brother - that's something you dream of as a boy. There are lots of positives to take from this."
Additional reporting by the Press Association
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