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France bounced back from Haris Seferovic's first-half opener for Switzerland thanks to a fantastic quick-fire brace from Karim Benzema.
Manchester United star Paul Pogba curled in a stunning strike past Yann Sommer to put France 3-1 up in the second half on Monday.
However, France's lead slipped away after Seferovic and Mario Gavranovic levelled the scores and sent the last-16 clash into extra time.
Neither side broke the deadlock in extra time before the match went to a penalty shootout, with Kylian Mbappe missing his decisive spot-kick effort.
Speaking after France's Euro 2020 exit, Mourinho has suggested that Deschamps made a big mistake in replacing Antoine Griezmann with Moussa Sissoko late in the second half.
The 58-year-old Portuguese manager admitted that he thinks of a mistake like that "many, many times," especially if the match will move into the extra-time phase.
Mourinho told talkSPORT: "I believe France had a little bit of fun, which in football I think you must have football after the game, not during the game. They had fun too early.
"They were playing fantastic, the way they changed the result, amazing, Benzema's first goal was incredible, Pogba's third goal was top. But then I think they had a little bit of fun.
"I also believe Deschamps made one mistake that I think about many, many times.
"When you're in a game where there's a possibility of extra time, you have to be very careful with the changes you make.
"When you make a change on minute 89 and you take off one of your best players, Griezmann, who was playing amazingly well and you change Griezmann for Sissoko.
"If this is a points game without extra time, that's okay. But when there's the possibility of extra time that's a big game because then you make that change, they equalise in minute 91 or 92, you go to extra time and then you want to shoot yourself because you left Griezmann out of extra time.
"Then in extra time you have the unlucky situation you cannot control of Benzema getting injured or feeling something and you lose your two top attacking players.
"And then during extra time you never felt France could win it because they didn't have the power to do it.
"I think in this moment that Deschamps knows he made that mistake, which is something that can happen to every one of us, but experience helps us.
"When you have extra time as a possibility still open you don't take off one of your best players."
Mbappe has since broken his silence over his penalty miss by apologising to France fans on Instagram, saying that he "failed" the 2018 World Cup champions.
Meanwhile, Brazil legend Pele has sent a classy message to the 22-year-old Paris Saint-Germain superstar on social media.