Elaine Flannery, from Blarney in Co Cork, died in October 2014 from metastatic cervical cancer, aged 59.
She had a smear test under the national cervical check screening programme in November 2010, which was reported as having no abnormality detected.
Two years later, she was diagnosed with invasive cervical cancer.
Today's settlement in the sum of €675,000 was made without admission of liability after mediation.
Senior Counsel Patrick Treacy said it was a source of enormous distress to the family that they did not receive an apology.
Mr Treacy said their case was based on a number of expert reports, which said the smear slide taken in 2010 showed "very obvious high grade lesions", which were indicative of an already established cancer.
The slide was also reviewed by the Royal College of Obstetricians and Gynaecologists, which reported that had the cancer been detected and a referral for treatment made her condition could have been prevented.
Mr Treacy said the HSE had referred to its own expert review, which reported the slide as negative and while he accepted that report was "written in good faith", the case was settled without admission of liability and therefore no apology was made.
Ms Flannery's husband David, and her five adult children, including the singer/songwriter Mick Flannery and two grandchildren, were in court for the settlement.
Mr Justice Coffey also approved the statutory sum in cases of wrongful death of €35,000 to be divided among the family.
The judge said Ms Flannery's death was "tragic and sad" and he had no doubt about the effect it had on her husband and children.
In a High Court action it was alleged there was a failure to correctly report and diagnose her smear sample taken in 2010 and her cancer was allowed to develop and spread untreated for two years.
It was further alleged that had her illness been detected in 2010 she would have been successfully treated with surgery and chemotherapy.
Ms Flannery's family said tomorrow marks the eighth anniversary of her death.
Outside court, Eamonn Flannery read a statement on behalf of his father David, which said today's proceedings marked the end of a mediation process where there was a measure of financial compensation but "not one word of an apology".
He said the apology they sought was "a no-strings attached" one.
"Just a simple form of sorry for our enormous loss and for the heartbreaking pain caused would have sufficed," he said.
"For me personally, this unwillingness of the defendants to offer not one word of regret by way of sympathy beggars belief in its want of common decency. It angers me, as it does our children and Elaine's mother and siblings."
He added that the current practice of not offering an apology where one is clearly needed was "brutally inhuman in its scant regard for what is right and its ignorance of human psychology".
Mother of five and microbiologist Elaine Flannery from Blarney was just 59 years of age when she died from metastatic cervical cancer in October 2014. Outside the Four Courts her family stood as a statement was read out on behalf of her grieving widower, 70-year-old David Flannery.
Mr Flannery who had sued the HSE settled his action for €675,000 and the High Court was told the settlement is without an admission of liability. Liability was heavily contested in the case.
At issue in the action was a smear slide from Mrs Flannery taken in November 2010 under the CervicalCheck programme. Mrs Flannery was diagnosed with invasive cervical cancer in 2012 and died two years later. Her son, acclaimed singer songwriter Mick Flannery, was in court with his four siblings and father as the court was told of the settlement and how the family are distressed that there was no apology from the HSE.
Outside court in a statement read out by his son Eamonn, Mr Flannery said: “What harm would it have done for the HSE to have said a simple sorry? Wednesday is eight years to the day since our beloved Elaine was taken from us. She had been bravely battling cancer for the best part of two years when she died 17 days after her 59th birthday.”
He said the legal proceedings marked the end of a mediation process where there is a measure of financial compensation granted to the family “but not one word of an apology.” Mr Flannery said they had sought “a no strings attached" apology.
Just a simple form of sorry for our enormous loss and for the heartbreaking pain caused would have sufficed.
“What harm would it have done for the HSE to have said a simple sorry? I won't pretend I know how they'd answer but we all know the good if would have done.” The Flannery family counsel, Patrick Treacy SC instructed by Cian O’Carroll solicitors, told the High Court the case had been settled after mediation.
The case was before the court for the ruling of the statutory €35,000 solatium mental distress payment. Counsel said the settlement was without admission of liability.
He told the court that experts on their side would contend that on examination of Mrs Flannery’s smear slide they found cells which one expert described as high grade. Counsel said it was their case that if Mrs Flannery had been referred for investigation and treatment in 2010 the cancer which was diagnosed two years later would have been prevented.
Counsel pointed out that a report on behalf of the US laboratory involved reported back that the slide was negative, and liability was at issue in the case. Mr Treacy said it was a source of great distress to the Flannery family that there was no apology in the case.
Mrs Flannery’s husband, maths lecturer, David Flannery of Blarney, Co. Cork, had sued the HSE. On November 11, 2014, Mrs Flannery had a cervical smear test under the CervicalCheck national screening programme.
Mother of five and microbiologist Elaine Flannery (pictured) from Blarney was just 59 years of age when she died from metastatic cervical cancer in October 2014.It was claimed that the cytology report from a US laboratory indicated the smear sample was satisfactory for assessment and there was no evidence of neoplasia or abnormality.
Two years later in October 2012, Mrs Flannery was diagnosed as having invasive cervical cancer. She underwent chemotherapy, radiotherapy and brachytherapy but died on October 26, 2014.
It was claimed that there was an alleged failure to correctly report or to diagnose and Mrs Flannery’s November 2010 smear sample was allegedly misinterpreted, and her cancer was allegedly allowed to develop and spread unidentified, unmonitored and untreated until she was diagnosed with cervical cancer in October 2012.
Had Mrs Flannery’s disease been detected in 2010, it was further claimed, she would have been treated by either radical surgery or chemoradiotherapy with curative content.
There was, it was contended, an alleged failure to advise, treat or care for Mrs Flannery in a proper, skilful, diligent and careful manner and an alleged failure to use reasonable skill, care and judgement when reviewing her smear sample taken on November 11, 2010.
Mrs Flannery, it was claimed, was deprived of the opportunity of timely and effective investigation and management of her condition and allegedly deprived of the opportunity of treatment at a time when her disease was amenable to curative treatment.
There was, it was claimed, an alleged failure to ensure the provision of a proper, efficient and competent cervical cancer screening service and an alleged failure to ensure that those providing the service possessed or exercised the necessary skill, experience, training or expertise to effectively report on cervical cytology and to detect the presence of changes in the cervix cells such as to ensure the early detection, prevention and treatment of cervical cancer in women, including Mrs Flannery.
All the claims were denied. Noting the settlement, Mr Justice Paul Coffey said it was a sad and tragic case and he extended his deepest sympathy to Mr Flannery and his family on their loss.