Archbishop Philip Tartaglia, who has temporarily taken over O'Brien's role as administrator of the Archdiocese of Edinburgh and St Andrews, on Monday told an evening mass that it was "a sad moment for the church in our country.
"The events around Cardinal O'Brien, his resignation, his statement of yesterday, have left us all very sad for everyone involved and for the Church," he said.
"Many reproaches have been aimed at the Church and at individuals over this matter.
"The most stinging charge which has been levelled against us in this matter is hypocrisy - and for obvious reasons.
"I think there is little doubt that the credibility and moral authority of the Catholic Church in Scotland has been dealt a serious blow and we will need to come to terms with that."
The 74-year-old O'Brien had been due to be the only British cardinal to vote on a replacement for Pope Benedict XVI following the pontiff's shock resignation on February 11.
O'Brien resigned last week in the wake of claims that he made sexual advances towards priests.
"In recent days certain allegations which have been made against me have become public," said the cleric in Sunday's statement. "Initially, their anonymous and non-specific nature led me to contest them.
"However, I wish to take this opportunity to admit that there have been times that my sexual conduct has fallen below the standards expected of me as a priest, archbishop and cardinal," he added.
Tartaglia, who said he would carry out the cardinal's former duties until a permanent replacement is found, vowed the church would not gloss over the crisis.
"We will draw what conclusions and lessons we can from it and, if anything, we will learn to trust even more fully in Jesus Christ who is alone the Lord of the Church," he said.
"We will not forget for a long time, but we will heal and we will carry on.
The allegations include claims that one priest received unwanted attention from O'Brien after a late-night drinking session, Britain's Observer newspaper reported last month.
Another priest reportedly claims that O'Brien used night prayers as cover for inappropriate contact.
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"The events around Cardinal O'Brien, his resignation, his statement of yesterday, have left us all very sad for everyone involved and for the Church," he said.
"Many reproaches have been aimed at the Church and at individuals over this matter.
"The most stinging charge which has been levelled against us in this matter is hypocrisy - and for obvious reasons.
"I think there is little doubt that the credibility and moral authority of the Catholic Church in Scotland has been dealt a serious blow and we will need to come to terms with that."
The 74-year-old O'Brien had been due to be the only British cardinal to vote on a replacement for Pope Benedict XVI following the pontiff's shock resignation on February 11.
O'Brien resigned last week in the wake of claims that he made sexual advances towards priests.
"In recent days certain allegations which have been made against me have become public," said the cleric in Sunday's statement. "Initially, their anonymous and non-specific nature led me to contest them.
"However, I wish to take this opportunity to admit that there have been times that my sexual conduct has fallen below the standards expected of me as a priest, archbishop and cardinal," he added.
Tartaglia, who said he would carry out the cardinal's former duties until a permanent replacement is found, vowed the church would not gloss over the crisis.
"We will draw what conclusions and lessons we can from it and, if anything, we will learn to trust even more fully in Jesus Christ who is alone the Lord of the Church," he said.
"We will not forget for a long time, but we will heal and we will carry on.
The allegations include claims that one priest received unwanted attention from O'Brien after a late-night drinking session, Britain's Observer newspaper reported last month.
Another priest reportedly claims that O'Brien used night prayers as cover for inappropriate contact.
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