Zidane, 34, told a French television station that Materazzi "deserved it" for insulting him with some "very hard words" aimed at sullying his mother and sister.
"I want to ask for forgiveness from all the children who watched that. There was no excuse for it," he said.
"I want to be open and honest about it because it was seen by two or three billion people watching on television and millions and millions of children were watching," he said.
Asked what exactly Materazzi had said, Zidane only said that it was "very personal and concerned his mother and his sister."
"You hear those things once and you try to walk away. That's what I wanted to do because I am retiring. You hear it a second time and then a third time ..."
Zidane was not asked in the interview whether there was a racist tone to the insults.
"I can't say I have any regrets about what I did because that would be like admitting that he had every reason to say what he said." said Zidane.
"I can't, repeat can't say that. He had no reason to say what he said. It's always the reaction that is sanctioned and not the provoker."
The French skipper was given a red card after delivering a headbutt to Materazzi's chest in the second period of extra-time in Sunday's final in Berlin, his last game before retiring.
Italy went on to win the World Cup on penalties after the match had finished tied at 1-1 after extra time.
The headbutt spurred much probing, with some television stations hiring lip-readers to work out what was said.
All agreed that Materazzi had insulted the Frenchman immediately prior to the headbutt, but what he actually said has been mired in mystery.
Theories ranged from insults against Zidane's mother, sister and family to him being accused of being an Arab terrorist.
But Materazzi refuted all those claims, and denied he said anything about Zidane's mother, in an interview with Italian newspaper Gazzetta dello Sport.
"I did not say anything to him concerning racism, religion or politics," said the Inter Milan centreback.
"I didn't say anything about his mother either. I lost my mother when I was 15 years old and still now nothing moves me more than talking about her.
"Naturally, I did not know that his (mother) was in hospital and I want to send her my best wishes.
"Zidane has always been my biggest idol, I admire him a lot."
Zidane had been silent over what had made him lose his cool until Wednesday's delayed broadcast interview with popular Canal + television sports presenter Michel Denisot.
"Do you imagine that in a World Cup final like that with just 10 minutes to go to the end of my career, I am going to do something like that because it gives me pleasure?" he said.
World football's governing body FIFA has launched an investigation into what happened and its chief Sepp Blatter said on Wednesday that Zidane could lose his award as best player of the tournament.
Zidane, who was born and grew up in Marseille, is the son of Algerian immigrants and has suffered taunts about his heritage throughout his football career.