The defender was dismissed for a kick out at the Corinthians striker shortly before the final whistle in the Club World Cup final.
The 26-year-old told Sky Sports News: "He lashed out with his arm and hit me in the face. Someone's smashed me in the face but I didn't roll around on the floor for five minutes holding my head.
"I got up, reacted and tapped him in the shin. He felt the need to go down, roll around on the floor for about five times holding his face.
"It probably is a red card but the reaction of the guy is totally out of order for what I did if you see the impact. It wouldn't have been enough to knock over my one-year-old daughter."
Cahill will serve a one-match ban, meaning he will miss Chelsea's Capital One Cup quarter-final against Leeds United on Wednesday.