Michelle and Barry Rocks contacted UTV after it revealed failures in the treatment of another baby at the same hospital.
Michelle was overdue when she was admitted to the Causeway Hospital on 25 June last year, but by 3pm the next day it emerged that there were problems with baby Cara's heartbeat.
"Their faces whenever they just couldn't find the heartbeat again after they broke my waters, they were just in pure shock," Michelle said.
"I think there maybe was about at least 10 people at the bottom of the bed at that stage, all panicking."
An emergency caesarean section had to be carried out but Cara was stillborn.
"I just couldn't believe it you know, I couldn't even hold her right away because I just couldn't believe it," Cara's dad Barry said.
"Michelle at this stage was still unconscious and then I had to go in and tell Michelle what she thought. I went in to tell Michelle and Michelle opened her eyes I just said to her, 'you know it has happened don't you', and she said 'yes, Cara's dead'."
Michelle had expressed concerns about the pregnancy, including the position of her baby, and had wanted a planned caesarean section - but she said she was refused.
"We were in and out of the hospital several times and I raised concerns, things should not have went so wrong, there's definitely fault here," she added.
The death was treated as an adverse incident and a case review found that Michelle should have been reviewed by a senior obstetrician, the result of which may have been a caesarean section that could have prevented the baby's death.
The pregnancy was described as low risk but given Michelle's history, the review found that was wrong.
The Northern Trust found that there seemed to be genuine lack of situational awareness, with the staff reluctant to believe what was happening. It concluded that there had been missed opportunities.
On Friday, the Trust identified 20 separate incidents over a five-year period, from 2008 to 2013, where the response had been "below standard". The Northern Trust confirmed that Cara's death is one that is being investigated.
"The Trust admits that its handling of this case fell short of the standard that Ms Rocks should have expected in the care of her daughter," the statement said.
"For this the Trust is truly sorry and apologises unreservedly."
The spokesperson said a full review was carried out and recommendations implemented.
Michelle has said that serious changes are needed within Northern Ireland's health system.
"The wrong decisions were made and they have said if I had been taken to theatre she would have been, she would have been alive, if I had a section, it's just hard to take in," she said.
"Something has to change, wee babies and families can't keep going through what we have gone through and lots of other families have went through. Something has to change, something has to be done, answers are needed badly."
Earlier on Wednesday, Health Minister Edwin Poots apologised to the McAuley family who lost their new born daughter because there was no theatre available to perform an emergency section.
He added that he regretted that "it has happened in other cases since" the death of baby Erin almost six years ago.
The Trust also apologised unreservedly to the McAuley family.