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.
"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."
"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."
