France were in complete control of their Group E clash in Salvador, racing to a 3-0 lead at half-time before Didier Deschamps' men added a further two goals during a six-minute period midway through the second half.
Switzerland salvaged some pride, scoring two goals in the final nine minutes courtesy of substitute Blerim Dzemaili and Granit Xhaka.
Speaking post-game, Hitzfeld said Switzerland did not play at the required level as they slumped to just their second defeat in 20 games.
"It was a black day for the Swiss team," Hitzfeld told reporters after Switzerland conceded five goals in a match for the first time since losing 5-0 to Norway in a World Cup qualifier in 1997.
"The two goals after a good first quarter of an hour killed us.
"We did not play to the level that we should have today. At 2-0, it became very hard for us, the French then logically exploited our mistakes to bring on more danger."
While France are on the verge of qualifying for the knockout phase after recording back-to-back wins, Switzerland remain in contention to advance.
Switzerland (-2) are level on three points with Ecuador (+0), though the South American nation occupy second spot in Group E on goal difference.
But the Swiss can move second in the standings if they beat Honduras in their final group game and Ecuador fail to defeat France, and Hitzfeld has not given up hope of reaching the round of 16.
"It's important that the team sticks together and doesn't start blaming anyone or let their heads hang," he said.
"That's why it was enormously important that we reacted in the second half.
"With the two goals we're still full of hope that we can make it to the next round. I want to say emphatically that qualification for the knockout stages is still within our reach.
"We have our destiny in our hands, we will analyse this match and bounce back - we lose together but we win together."
