It wasn't harsh criticism by Deschamps... and it wasn't public. According to the article, he took him aside for 20 mins after practice and was very animated when talking to him.
The thing Martial needs to realize with France at least is that his competition is very stiff. You have Griezmann, Payet, Fekir, Ousmane Dembele, Kingsley Coman and even Moussa Sissoko fighting for 2-3 spots on the pitch (depending on 433 or 4231). Before the Euro, Martial was the regular opposite Griezmann. Now, he's behind Griezmann, Payet, Sissoko and Coman. Fekir and Ousmane Dembele are just as talented as he is. So Deschamps wanted to make clear to him where he stood and why he keeps falling down the depth chart.
He's going to have to fight very, very, very hard to even stay on the France team, let alone become a regular. There's a lot of extremely talented kids pushing up too such as Mbappe and Lemar of Monaco, Augustin of PSG, Coco, etc. Deschamps gave him notice.