The Atletico Madrid forward, who recently announced he will stay at the club despite interest from La Liga champions Barcelona , was substituted before the hour mark and did not look happy following France's lethargic display.
As France look ahead to Thursday's showdown with Peru in Ekaterinburg, head coach Deschamps was asked about Griezmann and justified his decision to withdraw the Europa League winner.
"He is well. There was a little concern with one of his ankles as it was swollen after the game. He's trained as per usual," Deschamps told reporters on the eve of France's second match.
"He wasn't at his best during the match. He had heavy legs but it happens. He scored the goal and [we] decided to get him out so we could have something extra he couldn't provide. It didn't impact the result.
"If he stayed on the pitch and the result was different, you would've asked me the opposite question. The substitutes brought us something different."
France, and particularly their front three, were heavily criticised after the match against Australia but Deschamps appears set to retain faith in Griezmann, Kylian Mbappe and Ousmane Dembele, despite the qualities of Olivier Giroud.
"We will see tomorrow [Thursday]. The problem with Olivier, he plays alone," Deschamps said. "He isn't the same as others but when he's not there, we realise how useful he is. He is capable of starting."
Although France received significant criticism, other World Cup favourites have also struggled. Reigning champions Germany were beaten by Mexico in their first match, while Brazil and Spain were both held to draws.
Deschamps, who acknowledged France can and must do better against a talented team in Peru, added: "I saw many teams who would've liked to have the same difficulties as us and the same result."
Peru's all-time leading scorer Paolo Guerrero is set to play a key role for his country, who lost their opener 1-0 to Denmark despite controlling much of the proceedings.
Guerrero, who came off the bench in that game, was set to miss the World Cup due to a doping ban but he was granted the chance to represent his country thanks to some help from France captain Hugo Lloris, Australia's Mile Jedinak and Denmark skipper Simon Kjaer.
The trio of captains signed a letter pleading for Guerrero play at the World Cup.
Asked about the gesture, Lloris said: "Being able to play at a World Cup is unique and very special for a player's career and it's the case for him.
"It was only an act of solidarity for a player who was punished but who didn't try to cheat or boost his own performance. The decision was taken by higher authorities. I don't want to go into details but it's the will of the other captains. It was a simple act."