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Haris Seferovic put the home side ahead inside 55 seconds and it was the only goal of the game, which frustrated Fernando Santos' side.
Portugal won the reverse fixture 4-0 last week but didn't have it all their own way out in Lancy.
Fernandes played 74 minutes and if you follow the Premier League, you'll know the Manchester United star is prone to losing his rag.
In the 91st minute, Switzerland defender Nico Elvedi and Portugal forward Andre Silva came together and it resulted in a Switzerland free-kick.
The Portugal bench believe Elvedi went down far too easily and it was Fernandes who protested the most.
Cameras picked up the 27-year-old shouting at Switzerland players and staff with some colourful language thrown in for good measure.
Defeat was Portugal's second in Nations League history and they were beaten by the quickest goal in the competition's short tenure.
Seferovic headed home after rising above the Portugal defence and Murat Yakin's men did a good job of frustrating Portugal from then on.
Goalkeeper Jonas Omlin was in fine form and managed to keep out a Danilo Pereira drive plus an effort from Bernardo Silva.
He also stopped a Diogo Jota header while Joao Cancelo bent his strike over.
Santos was furious with the referee's performance at full-time and referenced the tackle on Silva, which the RB Leipzig man needed treatment for.
"I'm not going to criticise, but when a penalty is awarded that doesn't happen just like that, when there's a clear foul in midfield... Then just look at the number of fouls and time lost," he vented to reporters.
"The fourth official knows very well what happened in the game."
Portugal were without talisman Cristiano Ronaldo, who was rested, and they missed his clinical edge up top.
Veteran coach Santos continued: "At half-time, I was just saying that we have to have the ball and play differently and push them back.
"We started very well, in the first few minutes we wanted to put the ball very quickly on [Goncalo] Guedes. We knew opportunities would arise and many have arisen."
Portugal return to action in September against the Czech Republic.
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