The Blues became the first European Champions in six years to not win the competition as they lost 1-0 to South American champs Corinthians with Cahill seeing red late after an altercation with forward Emerson.
"He lashed out with his arm and hit me in the face," Cahill told reporters.
"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."