Zidane, then captain of France, was sent off for driving his head into Materazzi's chest before Italy won the final on penalties. Zidane, now France coach, said last month that he was not proud of the headbutt but did not regret it.
Materazzi said the incident, one of the most infamous in World Cup history, still troubled him 20 years later.
"The death of Jesus de Miguel made me thank God that nothing had happened to me," he told Italian outlet La Gazzetta dello Sport in an interview published on Thursday.
Tenerife striker De Miguel died after colliding with Andorra keeper Jesus Owono during a Segunda Division match earlier this month.
The former Everton and Inter Milan defender said he and Zidane appeared to put the episode behind them when they met before a match in 2010, although Zidane later denied the encounter had unfolded as Materazzi described.
"When he saw me, he hesitated a little, he even turned to walk back," said Materazzi.
"But I approached him and shook his hand: ‘I’m glad we’re meeting here, where nobody can see us.’
"He replied: ‘Don’t worry, these things happen, it’s all in the past.’ It’s a shame he later denied everything, saying he thought I was a fan."
Zidane's France play Italy in the Nations League later on Thursday.
