Suarez waited seven days before using his Twitter account to apologise to Chiellini and "the entire football family" for his actions during Italy’s Group D match with Italy on June 24.
"Suarez has shown he is humble enough to admit an error, which is very important," Zubizarreta told reporters.
"He has been humble enough to apologise to those he has affected, because it happened in the middle of a festival of football. In this case it's the best thing a person can do."
Suarez has been heavily linked with a move to Barcelona and Zubizarreta, who was speaking at the Nou Camp as the club unveiled Ivan Rakitic, made no secret of his admiration for the Liverpool striker.
"Everyone knows that Luis is an excellent player," he said.
"Everyone knows last season he played in various positions in attack, but everyone also knows that he is a Liverpool player."
Sky Sports' Spanish football pundit Guillem Balague believes Suarez had to apologise in order to secure his dream move to Barcelona.
"Barcelona wanted Luis Suarez to apologise," he said. "It is also part of an appeal that will surely reduce his ban.
"I realise many people feel cheated as he has apologised before. Biting shouldn’t be done but can be corrected and Chiellini has accepted the apology, so who are we not to do the same?"
Croatian international midfielder Rakitic added: "The fact he has had the character and the strength to go in front of everyone and say sorry says a lot about him as a person.
"I rarely say that I am wrong so this says a lot about him, he has shown the character and strength he has so he should be commended for that.
"Regardless of whether the club signs him or not, his quality is unquestionable.
"He has shown a lot of quality with Uruguay and scored more than 30 goals (last season) with Liverpool, so he has the necessary quality to play for Barca."