Mark and Róisín Molloy’s son, Mark, died soon after birth at Portlaoise hospital in January 2012.
Mr Molloy said it would be difficult to have faith in the “same people who brought us to where we are today” implementing the recommendations in the report.
“We have been waiting for this report since January 25th, 2012, the day after Mark died and the questions began. What’s in it is no news to us, but to have a panel of international experts draw the same conclusions as we have been screaming about for three years, well, there is vindication in that.
"But this is only a step in the process. What we need now is to get the managers and governance within the hospital and the HSE, who knew all this was going on and stood by, before the Oireachtas health committee to start answering the hard questions. If the committee's not happy, well, then we are looking at a public inquiry," said Mr Molloy.
He said he and his wife felt they had been “on a solo run” for two years and they had “worked within the system”.
“We thought we were telling people, at hospital level, local and national level, things they didn’t know, and it turns out they did and they stood by and allowed further unnecessary deaths.
"It was then we felt we had to go to RTÉ, when no one was doing anything. "
Joshua Keyes-Cornally, son of Shauna Keyes and Joseph Cornally, died at the hospital in 2009. Ms Keyes said yesterday she hoped there would be some "professional accountability and disciplinary action, now". It was clear to her and her family where the fault lay and it was "of course" at senior levels in the hospital and HSE.
“I have forgiven them a long time ago and I want people to do well at their job. That’s not going to happen while we are firing at them constantly. So I think now we need to take a step back and give them a chance to discipline people.
“If that doesn’t happen, yes they do need to be brought before other bodies like the Oireachtas health committee or their own professional bodies.”
“The care was great until something went wrong. The way they treated us, you wouldn’t treat a badly behaved dog. It was inhuman. They wanted us and our dead baby out the back door as fast as possible.”
She would also now like to see well-resourced national patient advocacy service.
Oliver Kelly and Amy Delahunt, whose daughter Mary-Kate died in 2013, said they were confident in the Hiqa report but would not rest until reforms were implemented.
“We have just heard about recommendations ... it just feels at times like the HSE are coming up with a ‘to do’ list, but nobody is actually going back with a checklist to see what’s being done and what’s being implemented,” said Ms Delahunt.
“It’s how the Minister and the chief medical officer react to the recommendations; [then] we will judge that as to whether it’s a success or not.”