The world champions let slip a two-goal lead against Switzerland before Kylian Mbappe's missed penalty saw them knocked out at the last-16 stage in dramatic fashion following a shootout.
Les Bleus had been the firm favourites going into the summer and, having fallen behind in the first half before rallying after Hugo Lloris saved a penalty from Ricardo Rodriguez, enjoyed a 30-minute spell playing to a standard which befitted their status, with Karim Benzema’s quick-fire brace and a goal of the tournament contender from Paul Pogba.
After falling remarkably short of expectations, the heat is now on Deschamps. But the France boss is not considering his future for now.
"That is not the question," said Deschamps, who has led his nation at four major tournaments - including to the final of Euro 2016 and World Cup glory in 2018 - and won two as a player.
"There is a unity and solidarity in this squad. I am responsible, when things go badly, I am with them, they are with me. We will need to time to manage this.
“We did what we needed to in order to go 3-1 up and then we showed weakness, something unusual for us. Losing on penalties is always cruel for a team."
Following Mbappe's miss from the spot, Deschamps added: “Kylian Mbappe is incredibly sad, as are all the players, but nobody can be upset with him as he took on the responsibility of taking the fifth penalty."
Haris Seferovic scored his second header of the night for Switzerland to make it 3-2 late on. Then, thanks to some horrendous defending, a visionary ball from Arsenal's Granit Xhaka and a fine Mario Gavranovic finish, the Swiss were level in the final minute.
France came close in extra time, Olivier Giroud had a header saved and Kingsley Coman hit the crossbar - but Switzerland went on to make history having never previously won a major tournament shootout.
"We wrote the history of this footballing nation," said Xhaka. "Now we have Spain in the quarters. It will be difficult, but we are dreaming now."
Xhaka - who is set to leave Arsenal for Roma this summer - was named man of the match, but the real hero was goalkeeper Yann Sommer, who made the crucial save in the shootout and says anything is possible ahead of the quarter-final meeting with Spain in Saint Petersburg on Friday.
"It was a really difficult situation for us after the penalty miss," said Sommer. "I’m really proud of the team, how they came back. We always believed. Even before the game we said no matter what happens, it doesn’t matter if we’re down, or if things are going well; we play until the end, we never give up.
"It’s always, ‘Anything is possible’. We believe. We said before the game that we are a small country, but we have a lot of quality and a lot of experience and we showed it tonight."