An inquest has resumed into the death of baby Darragh Byrne at the Coombe Women & Infants University Hospital in 2013.
The inquest has heard that the hospital had issued an apology to the family for the failings in the care of baby Darragh.
Barrister David Holland, for the family, told the inquest that the apology letter, dated November last, was issued in the last week and the reasons for this were unclear.
He said it was "extraordinary" that after the death, the hospital conducted no review.
"We want to be sure this dreadful tragedy does not happen to others," Mr Holland said.
Barrister Simon Mills for the Health Service Executive and the hospital said that once it became clear that the Master of the Coombe was not being called to give evidence, the apology letter was issued.
He said the hospital had not wanted to trespass on the coronial function.
The inquest before coroner Dr Brian Farrell is being held at the Dublin City Coroner's Court without a jury.
Baby Darragh was born to the Byrne family from Portlaoise on 15 February, 2013 and died on 19 February at the Coombe.
His mother, Maree Butler, told the inquest she had been attending Midland Regional Hospital, Portlaoise for ante-natal care and had gestational diabetes.
She said she was admitted to the Coombe at 35 weeks after her waters broke on 14 February, 2013.
She said she was advised that hospital policy was not to induce at 35 weeks and that she would deliver the baby herself.
Mrs Butler said she was very uncomfortable and in pain, the CTG (cardiotocography) machine kept going off and she was pushing for what seemed like an eternity.
Doctors told her she needed to go to theatre for a caesarean section.
"I was terrified and excited I was going to see my baby", she told the inquest.
After Darragh was born, she said he was blue and not responding.
Darragh's father Eoin Byrne told the inquest his son was a strange colour when born and very quiet.
He was presented to him in an incubator.
Mr Byrne said he cried his heart out in the hospital car park and could not tell his wife Marie all that had happened.
Baby Darragh was placed on a cooling mat to try and reduce swelling on his brain.
At a later stage, doctors said he had no brain activity.
'Doctor should have been called to review the labour' - Dr Michael O' Connell
Dr Michael O' Connell said he was the on-call consultant obstetrician and gynaecologist at the Coombe at the time.
Mrs Butler had not been his patient.
He told the inquest that the CTG scan which gave the foetal heart rate had been hard to read for an hour to an hour and a half before delivery.
He said that looking back now, the CTG shows little snippets of foetal tachycardia (an abnormal heart rate) and the Ph acid-base levels were very low.
Dr O'Connell said a doctor should have been called to review the labour.
He said that during labour, Mrs Butler had been uncomfortable and needed analgesia.
He said progress was slow in the delivery and he prescribed oxytocin, to speed up delivery.
He disagreed with lawyers for the family that he had breached the Coombe guidelines on oxytocin by using it in a pregnancy under 37 weeks.
Lawyers for the family said that oxytocin can interfere with the transfer of oxygen to the foetus and needs to be carefully monitored.
Dr O'Connell said foetal distress was suspected, Mrs Butler was taken to theatre for a possible instrument delivery or emergency caesarean.
The inquest heard that 54 minutes elapsed, between the time a decision was made to expedite the delivery, which was an emergency, and the section being performed.