Television cameras captured a frustrated Deschamps attempting to give the Manchester City forward instructions during the break in play, only for Cherki to wave his hand dismissively, turn his back on the France manager and walk away. Cherki was substituted at half-time, having endured a quiet first 45 minutes, and was replaced by Ousmane Dembele.
Deschamps declined to go into detail about the incident when asked after the match, choosing instead to focus on broader themes as he prepared to depart the France job after 14 years in charge.
"I'm not going to settle scores today," he said. "The players know exactly how things stand. I'm not going to point fingers.
"But as Kylian (Mbappe) also said, the players needed time to process it. It was my mistake. I should have made some different choices from the start of the match.
"That much can be said, and maybe it would have gone better. Everyone is judged on their performance. It's clear some players could have done better. I wish them all the best."
It was not the first apparent friction between the pair during the tournament. During France's last-32 win over Sweden, Cherki was also caught on camera seemingly ignoring Deschamps as he prepared to come on as a substitute.
The playmaker's frustration is understood to stem from limited game time throughout the World Cup, having largely been used sparingly behind Michael Olise and Bradley Barcola in France's attack.
The tension added to a difficult night for France's dressing room, with midfielder Adrien Rabiot separately delivering a pointed criticism of several team-mates after the match for what he described as a lack of respect for the shirt during a chastening first-half display.
The France camp had endured a bruising few days following their semi-final defeat to Spain, and the combination of a poor start against England, Cherki's touchline reaction and Rabiot's post-match comments painted a picture of a squad struggling to process the disappointment.
Deschamps' reign ends with the defeat, bringing down the curtain on 14 years in charge that included the 2018 World Cup triumph and a run to the final in 2022.