Pell was giving evidence from a hotel in Rome via video-link to the Royal Commission into Institutional Responses to Child Sexual Abuse rather than appear in person in Sydney as he has a heart condition.
The inquiry is currently focused on the Victorian state town of Ballarat, where Pell grew up and worked, and how the Church dealt with complaints against priests, many dating back to the 1970s.
Pell, who rose to be the top Catholic official in Australia, said the Church historically made grave errors in not properly addressing the issue and was now working to remedy them.
"Let me just say this, as an initial clarification, and that is I'm not here to defend the indefensible," he said after swearing on the Bible to tell the truth.
"The Church has made enormous mistakes and is working to remedy those. The Church in many places, certainly in Australia, has mucked things up, has let people down."
He acknowledged that in the past the Church's general attitude to abuse was that it was "much, much more difficult for the child to be believed" and complaints were often dismissed.
"I don't have the statistics on that but too many of them certainly were dismissed and sometimes they were dismissed in absolutely scandalous circumstances," he said, adding that the instinct was to protect the Church from shame.
"They were very, very, very plausible allegations made by responsible people that were not followed up sufficiently."
But he denied the Church's structure was to blame for the way it handled paedophile priests, despite counsel assisting the commission Gail Furness saying many inquiries around the world had found those in senior positions did not take proper action.
"I don't think it calls into question the divine structure of the Church which goes back to the New Testament, the role of the pope and bishops," he said.
"I think the faults overwhelmingly have been more personal faults, personal failures rather than structures."
Catastrophe for the Church
Pell has always denied knowing of any child abuse occurring in Ballarat, including by Gerald Ridsdale, seen as Australia's worst paedophile priest who preyed on dozens of children over two decades.
The pair shared a home but Pell has dismissed claims he helped move him to another parish or that he tried to buy anyone's silence. He told the commission the way Ridsdale was dealt with by church officials was "catastrophic".
"I have just re-read the file of Ridsdale. The priest - ex-priest - and the way he was dealt with was a catastrophe. A catastrophe for the victims and a catastrophe for the Church," he said.
"If effective action had been taken earlier, an enormous amount of suffering would've been avoided."
Pell also denied being aware of paedophile priests being sent for treatment for their sexual offending by then bishop of Ballarat Ronald Mulkearns while he was based in the diocese.
A group of survivors of abuse by Catholic clergy in Australia have travelled to Rome to hear Pell's evidence, which is expected to span three days, after a crowdfunding campaign to get them there.
"We want the truth. We want to be able to save more lives from too many suicides in Ballarat," survivor Dominic Ridsdale, a nephew of Gerald Ridsdale, told national radio.
Australia ordered the Royal Commission in 2012 after a decade of growing pressure to investigate allegations of paedophilia across the country.
It has heard claims of child abuse involving churches, orphanages, community, sports and youth groups and schools.