On a hot and humid night at the Olympic stadium, Les Bleus, who face European and world champions Spain in Donetsk on Saturday, were undone by a sublime Zlatan Ibrahimovic strike and a late goal from Sebastian Larsson and finished second in Group D behind England.
"We were prepared for tough game," France coach Laurent Blanc told reporters. "We didn't expect it to be so difficult. We were not strong enough in the tackles.
"I think Sweden played with lot of heart they gave everything, physically much better than us.
"In their ranks have a player could can make a difference in a game," Blanc added. "If we analyse the game I think we struggled throughout."
The result, which ended a 23-match unbeaten run, brought France down to earth after a convincing 2-0 win over co-hosts Ukraine with the central defence looking very shaky once again.
Captain Hugo Lloris, however, pulled off a series of stunning saves to keep his team afloat after Ibrahimovic had sent a superb volley into the net in the 54th minute.
Blanc's defensive puzzle may have been solved by Philippe Mexes himself, who had a night to forget but will miss the quarter-final through suspension.
At least, France will have a chance to redeem themselves after being knocked out in the first round of Euro 2008 and the 2010 World Cup amid off-pitch controversy.
They will clearly need to do that against defending champions Spain but they have shown they cannot be written off and have never lost a competitive game against the Spaniards.
In 2006, France struggled in the first round of the World Cup, but found their form to see off Spain in the last 16 and went on to reach the final.
France, who suffered their first defeat by Sweden since 1969, will know they can rely on the superb Lloris.
The keeper forced Ola Toivonen wide in the early stages after the striker was allowed to run free following a defensive blunder by Mexes.
France enjoyed long spells of possession but lacked sharpness and clearly missed the neat passing of Yohan Cabaye, who was rested in favour of Yann Mvila.
Hatem Ben Arfa, named in the starting lineup in place of Jeremy Menez, was a pale shadow of his normal talented self and was replaced in the second half as France looked extremely fragile.
The match swung Sweden's way when Ibrahimovic produced his magic moment and Erik Hamren's side continued to pile on the pressure.
Lloris denied Sebastian Larsson and Christian Wilhelmsson and although there was nothing he could do when the former thumped a volley into the net, he spared his team more embarrassment by diving at the latter's feet in stoppage time.
Karim Benzema, Mvila and Nasri all tried their luck but it was Franck Ribery who carried the main threat to the Swedish defence.
There was a minute's silence before kickoff in memory of French TV commentator Thierry Roland, a close friend o
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