Karim Benzema's brace and an own goal from goalkeeper Noel Valladares did for Honduras in their Group E opener, while Wilson Palacios was sent off before the break for a second yellow card following a clumsy foul on Paul Pogba.
Bernardez's injury added a further blow to a disappointing day for Suarez, with the San Jose Earthquakes defender appearing to twist his knee prior to half-time.
Suarez acknowledged France's deserved victory but felt that the result could have been different if Bernardez had played the full game.
"We expected no less (after Bernardez's withdrawal)," he told La Prensa.
"This is normal. Things would have improved if the team had been complete the whole game.
"(But) France deserved to win, unquestionably."
Honduras next face Ecuador on Friday, with both sides knowing that a defeat could end their hopes of progressing to the knockout stages.