The cardinal shocked the Roman Catholic community when he indicated that he would not contest claims against him and intended to retire permanently from the public life of the church.
His admission came a week after three priests and a former priest accused Britain's most senior Catholic of inappropriate behaviour dating back to the 1980s.
The cardinal, who has stepped down from his post as Archbishop of St Andrews and Edinburgh, has asked for forgiveness from those he had offended.
He said of the claims: "Initially, their anonymous and non-specific nature led me to contest them. However, I wish to take this opportunity to admit there have been times my sexual conduct has fallen below the standards expected of me as a priest, archbishop and cardinal."
The complaints have been reported to the Vatican, and a Scottish Catholic Media Office spokesman said: "We expect they will be investigated and a conclusion drawn." The inquiry is not likely to begin until after a new pope is chosen.
The cardinal, who was born in Ballycastle, Co Antrim, had been the Archbishop of St Andrews and Edinburgh since 1985. Ordained as a priest in 1965, he was proclaimed a cardinal by Pope John Paul II in October 2003.
One of Scotland's most outspoken opponents of same-sex marriage, he was last year named Bigot of the Year by gay rights group Stonewall.
The claims against the cardinal emerged last Sunday and the following day it was announced that he would quit his post with immediate effect.
The cardinal had been due to retire later this month when he turned 75 and the Scottish Catholic Media Office said his resignation had not been accelerated because of the allegations.
In fresh claims published yesterday, the anonymous former priest who reported Cardinal O'Brien over the allegations attacked the Church's response to the complaints.
He said: "There have been two sensations for me this week. One is feeling the hot breath of the media on the back of my neck and the other is sensing the cold disapproval of the Church hierarchy for daring to break ranks. I feel like if they could crush me, they would.
"The vacuum the Church has created has allowed whimsy and speculation to distort the truth, and the only support I have been offered is a cursory email with telephone numbers of counsellors hundreds of miles away from me."