Mourinho revealed his anger at an unnamed player after Wednesday's 1-1 draw at Sassuolo, a result that came after their 1-0 defeat at Lazio in the Rome derby, telling him to find a new club in the January transfer window.
While Mourinho did not name the player, reports in the Italia media said that it was Netherlands defender Karsdorp, who came on as a substitute in the 65th minute.
"We are surprised at Mourinho's statements, which point to Rick, without Mourinho or AS Roma mentioning Rick's name. We want an explanation from the club about the trainer's words and how he did it," Henkes told Dutch public broadcaster NOS.
"That's not how you treat a player who has been playing for AS Roma for five years."
Karsdorp, 27, looked out of position and left forward Armand Lauriente unmarked in the build-up to Sassuolo's goal.
"I'm sorry, because the team's effort was betrayed by the attitude of an unprofessional player," Mourinho said.
"I feel betrayed by one of my players. He betrayed everyone else. Who is it? I won't say. In January he will have to find another team."
A former Feyenoord player who has made three appearances for the Netherlands, Karsdorp is under contract with Roma until June 2025.
"The mistake is part of the game," Mourinho said. "The unprofessional and incorrect attitude with the teammates displeases me. I already said it [the name] in the changing room, and I don't do that often.
"After matches, I don't speak often with the team. I had 16 players on the pitch, I liked the attitude of fifteen. I didn't like one and I said so."
Roma are sixth in Serie A, 12 points adrift of league leaders Napoli after 14 games.