Mbappe was with the French squad for the Nations League matches over the past week, but was sent home after he tested positive for the virus, with him now self-isolating.
Paris-Saint Germain reportedly found out about the test through the media, which enraged sporting director Leonardo.
"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.”
The Brazilian would later accuse the FFF of a lack of respect towards the Champions League finalists.
However, Deschamps has attempted to explain the situation and blamed the media for the news leaking.
"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," L'Equipe quoted him as saying.
"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."
Even with the absence of star player Mbappe, France won their two Nations League matches, defeating Croatia 4-2 and Sweden 1-0 respectively.
The Frenchman is now one of several PSG players who have tested positive for the virus over the past week, with Neymar, Leandro Paredes, and Angel Di Maria forced into isolation after returning from Ibiza.