Mbappe was withdrawn from the France squad after testing positive for Covid-19, but Les Bleus were still too strong for Croatia with a 4-2 victory in the Nations League on Tuesday.
Leonardo was unhappy to hear about the PSG star's positive test through the media and felt the Ligue 1 champions had been disrespected.
But Deschamps dismissed any suggestions France had been disrespectful, saying they were rushed into releasing the confirmation.
"I will be factual. At the end of the training session, Kylian has a positive test. We deal with the most in a hurry by isolating him from the rest of the group," he told a news conference, via L'Equipe.
"At the same time, 10 tests are pending and are arriving in dribbles. We arranged for Kylian to be taken care of so he could go home.
"I would add that for all the players who test positive there is a need for confirmation from the laboratory, which takes time, because they re-analyse. We have this confirmation around 10pm. In the meantime, one of you has released the info.
"So that it does not go all over the place, we decided to issue a press release. That's what happened. We were in a hurry. There was little doubt, but we were supposed to wait for confirmation. I don't think I disrespected anyone."
Leonardo made the accusations against the French Football Federation on Monday, insisting the lines of communication had broken down surrounding Mbappe's diagnosis.
"I find it completely unacceptable that we learn from the press that one of our players is positive,” he told RMC. “They released a statement and sent the player home but no-one from the Federation has communicated this to us. No one has contacted us.”
Asked if he was forced to call the player to receive the communication, he said: “Exactly. He is at home and we learned that from him.
"Are we managing? Everyone gives lectures to PSG, that we’re poorly managed. But when this happens, it's still PSG that have to manage the problems, despite not knowing about them. PSG are always the bad guys in the story.
"It is a lack of respect to never communicate with the club. We did not speak with anyone. We only spoke with Mbappe. We were the ones who had to put the pressure on. It is unacceptable."
Mbappe is set to miss PSG's opening Ligue 1 game of the 2020-21 season against Lens on Thursday.