The archbishop admitted the number of people attending Mass had dwindled in the wake of changing structures and scandals.
But he insisted the church had a future, as he celebrated a special Mass in aid of Dublin's Catholic University School (CUS).
The comments come in the wake of the damming report of the Commission of Investigation into the Catholic Archdiocese of Dublin.
The three-volume report, which covered the period 1975 to 2004, found that clerical child abuse was covered up by the Archdiocese of Dublin and other church authorities.
Pressure is now mounting on five sitting bishops, who were named in the report, to resign their positions.
Dr Martin recently wrote to the Bishop of Limerick Donal Murray and others to say he was not happy with their response to the findings.
Integrity
During his sermon at St Teresa's Church in Grafton Street, Dr Martin preached the need for integrity and called on people to retain their faith.
"I say especially to young people: do not abandon the Church. Your Church lies in the future," he told the congregation. "You will provide something special so that the arrogance of the past can be replaced."
During the prayers of the faithful, students and teachers asked God to help those who had suffered neglect as children.
They also prayed for God to grant all bishops and priests "the wisdom to know how to act and the courage to sustain their vocation".
Earlier, ordinary churchgoers insisted Dr Martin was doing a good job in the wake of the report and urged him to continue in his position as they made their way into Mass at St Mary's Pro-Cathedral in Dublin for morning services.
"I think Archbishop Martin is doing the best he can," said Tom Fitzpatrick. "I'm not sure the Pope is doing his best, though. He seems to be giving the cold shoulder to our archbishop."
Anne-Maire Russell insisted Dr Martin needed prayers from ordinary Catholics to guide him through the crisis.
"I think he is doing a wonderful job. He needs a lot of prayers," she said. "He has huge responsibilities and needs a lot of support."
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