Abuse survivor Louise O'Keeffe, who successfully fought the state over her suffering in school, has said the Taoiseach's apology was for all victims.
Enda Kenny said the 46-year-old's experience was indicative of a long litany of child abuse cases that had scarred memories.
Ms O'Keeffe this week won a landmark European Court of Human Rights battle to hold the state liable for her suffering after being sexually abused by her principal at Dunderrow National School in Co Cork in 1973.
"I appreciate very much his apology and I suppose I appreciate the fact that he did it quickly," she said.
"I would never have looked for an apology for myself.
"I would have looked for an apology for all victims of abuse in schools because there are many of them who have not come forward."
As the Government launched the new Child and Family Agency in Dublin Castle, designed to improve protection and welfare of children in all aspects of life, the Taoiseach took the opportunity to speak about Ms O'Keeffe's long-running battle.
"I would like to say to Louise O'Keeffe that I apologise for what happened to her in the location where she was and for the horrendous experiences that she had to go through," he said.
The state fought her claims and initially won in the High Court and Supreme Court in Dublin, before going on to the Strasbourg court where Ms O'Keeffe triumphed.
She told RTE Radio she would not have pursued the battle if she had been given an apology.
She urged the Government to act on the human rights judgment.
"I'm simply one of hundreds who have come forward and those who have not," she said.
"An apology is for everyone because I know I was not alone."
Tanaiste Eamon Gilmore also apologised during questions in the Dail.
The European court issued a lengthy judgment in Ms O'Keeffe's favour on Monday.
The landmark lawsuit against the Irish state could have massive ramifications for 135 other survivors of abuse in school, including in terms of compensation, who alleged similar liabilities.
Ms O'Keeffe's former principal Leo Hickey was prosecuted in the 1990s for historic abuse against pupils.
He was charged with 386 criminal offences of sexual abuse involving 21 former pupils of the school, near Kinsale, Co Cork.
In 1998, he pleaded guilty to 21 sample charges and was sentenced to three years in jail.
The European court found that Ireland's system of detection and reporting of abuse was ineffective in the 1970s as it allowed more than 400 incidents of abuse over such a long period.
It said if adequate action had been taken in 1971 when the first complaint against Hickey was made, Ms O'Keeffe might have not been abused by him.
Meanwhile, the new Child and Family Agency which has been officially launched will take over the role of three separate bodies to improve services for children, which the Government said was the most effective response to repeated and tragic failings of the past.
It will have 4,000 staff, a budget of 609 million euro and a national network of 106 community-based family resource centres and is being billed as a ferocious corporate parent demanding the best for the country's youngsters.
Gordon Jeyes, chief executive of the new agency, pledged it would tell it as it is when it came to child protection and services.
"This agency is an exciting fresh start, putting children first always: planning for individuals, joining up services," he said.
"One child. One plan. Many perspectives.
"The Child and Family Agency will be a ferocious corporate parent, demanding for the children of Ireland the very best that the state can give.
"This will be an agency that has the agility and the freedom and flexibility to engage with individual families on a practical level and the capacity to react to changing circumstances.
"This agency will tell it as it is."
The agency, tusla.ie, will take on work currently done by the Health Service Executive (HSE), the Family Support Agency and the National Education Welfare Board.
It will also offer care and protection for children in circumstances where their parents are unable to, and ensure every child in the state is being educated.
It will see social workers and staff in community-based services, education welfare and social care work in partnership with voluntary and other state agencies.
Expert s taff will deal with child protection and welfare, e ducational welfare, p sychological services, a lternative care, f amily and locally-based community supports and d omestic, sexual and gender-based violence services.