The 23-year-old winger was visibly upset following the quarter-final encounter in Rio de Janeiro, as Mats Hummels's first-half goal proved the difference.
"This is the biggest disappointment of my career," Griezmann told RTL. "I was proud to be here, it was dream but we have the [European Championships] to prepare for."
Of his on-pitch tears at the end of the game, which saw his teammates console him, the Real Sociedad man added: "I was told not to cry and to keep my head up high. Now it's time for vacation and rest."
France will take part in qualifying for Euro 2016, but as tournament hosts they are already assured of their place in the finals.