It added this would ensure that the complaints could "withstand challenge."
The church statement did not explain why either Cardinal Brady or his superiors at the time did not share their information with the police. Fr Smyth went on to abuse more children in the following years.
Delivering his St Patrick's Day mass on Wednesday, Cardinal Brady said: "This week a painful episode from my own past has come before me.
"I have listened to reaction from people to my role in events 35 years ago.
"I want to say to anyone who has been hurt by any failure on my part that I apologise to you with all my heart.
"I also apologise to all those who feel I have let them down.
"Looking back I am ashamed that I have not always upheld the values that I profess and believe in."
Cardinal Brady added that the church "must humbly continue to deal with the enormity of the hurt caused by abuse of children by some clergy and the hopelessly inadequate response to that abuse in the past".
Meanwhile, the Norbertine Community - which Smyth was a member of throughout his time as a priest - has said it is "deeply saddened at the controversy surrounding Cardinal Sean Brady".
"We again acknowledge our failure to remove Fr Smyth permanently from the exercise of ministry," it said.
"We apologise again to each and every person who was abused at any time by Fr Smyth, to their families and to the many others who suffered through these events.
"We apologise also for our failures to Cardinal Brady, to Bishop Leo O'Reilly and to the congregation and friends who have continued to support us here at the abbey."
Smyth was eventually convicted of dozens of offences against children.
Fr Brendan Smyth was convicted of dozens of offences
But despite allegations being previously investigated by church officials, including Cardinal Brady it was almost 20 years before he was brought to justice.
Northern Ireland's deputy first minister, Martin McGuinness has said Cardinal Brady "should consider his position".
He questioned how many other children were asked to stay silent.
However, NI Secretary of State Shaun Woodward said people should not "rush to judgement" on the issue.
Critics of the cardinal have accused him of colluding with clerical child sexual abuse and pressuring victims to remain silent.
The Rape Crisis Network Ireland (RCNI) said Cardinal Brady's position had become untenable.
Hundreds of allegations, many going back decades, of systematic child abuse by Catholic clergy have come to light this year across Europe.
The scandal has surfaced in Germany - Pope Benedict's homeland - Switzerland, Austria and the Netherlands.
Chancellor Angela Merkel said on Wednesday the only way to come to terms with it was to find out everything that has happened.
Describing the sexual abuse of children as a "despicable crime", Mrs Merkel said abuse was a challenge "for the whole of German society", and that it "made no sense" to focus solely on the Catholic Church.
She also said there should be a discussion about compensating victims and about lengthening the statute of limitations so that offences - many of which were committed decades ago - could be prosecuted.
Earlier, scandals have rocked the Catholic Church in the United States, Canada, Australia and Mexico.
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