"Common sense tells me that I don't need a rematch but my ego, my deep interior, tells me that this man needs to be punished," Klitschko, who won Saturday's fight on a unanimous points decision, told the online edition of Welt newspaper.
"I'd like to knock him out in the ring. The bill has not been paid."
Chisora was involved in a brawl with fellow British heavyweight David Haye at the post-fight news conference in Munich.
He also slapped Klitschko in the face and spat water at the face of his younger brother Vladimir, who holds the WBO, IBF, WBA and IBO crowns, during the pre-fight ceremonies.
"Before our fight, I thought that his behavior was all part of a show-act," said Klitschko. "Then I realized that he's not playing.
"He hit me in the face before the fight and spat at Vladimir in the ring. Then he got into a fight at the press conference and threatened to shoot someone.
"What kind of person can he be. Unbelievable. I can't grasp it. Everything I have experienced with him is as if I were in a nightmare."
(Writing by Brian Homewood in Basel; Editing by Ed Osmond)