Aired on BBC Northern Ireland last night (May 1), This World documentary The Shame of the Catholic Church focused on the Church's handing of clerical sex abuse allegations in the 1970s.
Cardinal Brady has resisted calls for him to resign as the primate of all-Ireland after This World claimed that he had names and addresses of those being abused by paedophile priest Brendan Smyth, but had not passed the details on to police or parents.
Dr Brady said that the BBC's allegations against him were "seriously misleading and untrue". He also said that the documentary-makers had set out to "deliberately exaggerate and misrepresent" his role in the scandal.
In a statement today, Cardinal Brady said that he was "shocked, appalled and outraged" by the actions of Smyth, who was later exposed as Ireland's most prolific paedophile.
"With others, I feel betrayed that those who had the authority in the Church to stop Brendan Smyth failed to act on the evidence I gave them," he said.
"However, I also accept that I was part of an unhelpful culture of deference and silence in society, and the Church, which thankfully is now a thing of the past."
Dr Brady is upset over what he claims is a 'serious misrepresentation' of his role on an inquiry team into allegations against Smyth in 1975.
The religious leader, who served as a notary for the team, said: "In the course of the programme a number of claims were made which overstate and seriously misrepresent my role in a Church Inquiry in 1975 into allegations against the Norbertine priest Fr Brendan Smyth.
"The commentary in the programme and much of the coverage of my role in this inquiry gives the impression that I was the only person who knew of the allegations against Brendan Smyth at that time and that because of the office I hold in the Church today I somehow had the power to stop Brendan Smyth in 1975.
"I had absolutely no authority over Brendan Smyth. Even my Bishop had limited authority over him.
"The only people who had authority within the Church to stop Brendan Smyth from having contact with children were his Abbot in the Monastery in Kilnacrott and his Religious Superiors in the Norbertine Order."
Father Smyth died in prison in 1997, just one month into a 12-year prison sentence.
This World: The Shame of the Catholic Church will be shown on BBC Two at 9pm on Wednesday.