The Scottish quartet were in command throughout against the Germans, leading 5-2 at the break before accelerating clear, but the hitherto unbeaten Swiss proved more obdurate opposition.
Mouat’s men led 3-2 at the break – a steal in the third proved the difference – and it took until the seventh end for either side to register a score greater than one.
It was the Swiss who did it, to lead 4-3, but it all came down to the last end.
Britain needed one to tie, two to win. They had to settle for the former, meaning an extra end. But Switzerland had the hammer and they held their nerve to close out a statement victory.
“On another day we come away with the win,” Mouat told BBC Sport.
“It’s going to be tough to beat them but we know we are playing pretty well and it would be exciting to play them again.”
Earlier in the day, Britain’s women were unable to repeat their statement win over Canada against the Swedish rink who denied them European gold in November.
The unbeaten Swedes raced out to a 7-3 lead at the break – after twice scoring three with the hammer – and stole one in the sixth to take a stranglehold on the game.
Rebecca Morrison’s rink kept fighting but ultimately fell to a 10-7 defeat to leave their semi-final hopes in the balance.
At least four wins will be required from their final five round-robin matches – starting against Denmark on Monday (08:05 GMT) – to have any hope of reaching the knockouts.
“It’s really hard at this level – it’s near-misses and we’re a couple of centimetres away from making great shots,” Morrison told BBC Sport.
“It’s frustrating but that’s what happens at the Olympics. You need to be at your best and we just weren’t quite there.”
The women are back on the ice against Denmark (08:05 GMT) and Switzerland (18:05) on Monday, while the men face Norway (13:05).