Mayfield said after the game that Callaway had been part of the Browns' game plan but noted that "things happen."
Kitchens wouldn't disclose why he chose to discipline Callaway.
"I don't know if he's gotten the message or not, but I'm not wavering," Kitchens told reporters in a conference call Monday. "But what Antonio and I talk about stays between Antonio and I."
Callaway was suspended the first four games of the season for violating the league's substance abuse policy. Since returning he has been the Browns' No. 3 receiver and has eight receptions for 89 yards and three touchdowns in four games.