The French captain repeatedly apologised to fans - especially children - in his first comments since Sunday's match, but said he did not regret the outburst that marked the end of his 18-year professional career.
"I tell myself that if things happened this way, it's because somewhere up there it was decided that way," the 34-year-old midfielder said in an interview on French television channel TF1 on Wednesday.
"And I don't regret anything that happened, I accept it."
He stressed that he felt no regret "because that would mean [Materazzi] was right to say all that".
"There was a serious provocation," said Zidane, who added that he had never had tensions with the Italian player before.
"My act is not forgivable," Zidane said. "But they must also punish the true guilty party, and the guilty party is the one who provokes."
Soft-spoken and relaxed in two television interviews late on Wednesday, Zidane did not explain exactly what Materazzi said that enraged him, but said it was about his family.
Zidane said Materazzi insulted his
mother and sister
"I would rather have taken a punch in the jaw than have heard that," he told the Canal Plus channel, stressing that Materazzi's language was "very harsh," and that he repeated the insults several times.
Zidane and Materazzi exchanged words after Italy broke up a French attack in extra-time. Seconds later, Zidane lowered his head and rammed Materazzi in the chest, knocking him to the ground.
He was sent off, reducing France to 10 men.
Italy went on to win in a penalty shootout with Zidane - who had scored a penalty earlier in the match and another one in France's semi-final win over Portugal - in the locker room.
Materazzi: Zidane my hero
Materazzi has acknowledged he insulted Zidane, without giving specifics.
At nearly the same time Zidane was on TV, excerpts from an interview that Materazzi gave were posted on an Italian paper's website, where he denied insulting Zidane's mother.
"I didn't say anything to him about racism, religion or politics," Materazzi told the Gazzetta dello Sport. "I didn't talk about his mother either. I lost my mother when I was 15 and even now I still get emotional talking about her."
Zidane "has always been my hero", Materazzi said. "I admire him a lot."
Zidane's World Cup and career
ended on a foul note
Despite the head-butt, Zidane was awarded the Golden Ball award for best player at the World Cup - although Sepp Blatter, the president of world football governing body Fifa has suggested Zidane could be stripped of the honour.
Fifa's disciplinary committee opened an inquiry on Tuesday into Zidane's behaviour.
Better known for his silky skills with the ball, Zidane was also no stranger to being sent off: He was shown the red card 14 times in his career at the club and international level.
Zidane, who retired at the end of the World Cup, said many people have asked him not to call it a day, but he said he would not change his mind.
"I won't go back on it, at least I hope so ... it's definitive," he said.
Zidane told TF1 that he was "going to rest, and then move on to something else".