Ranieri was reacting after their 2-1 defeat of Cagliari as Mourinho taunted him for showing his players 'Gladiator' before their defeat in the Coppa Italia final.
The Roma boss scoffed: "What film will I show them next time? Mickey Mouse. The information Mourinho has been receiving is not correct.
"I respect myself and others, but evidently Mourinho does not have this quality. I will not respond.
"He is a great Coach, a great motivator and that's all I'm going to say. At the same time, the media must stop fuelling the fire, as they changed what Mourinho said when reporting it back to me."