Dr Tan told the inquest said that pethidine is usually only used in the early stages of pregnancy because of the risks of respiratory problems if used in later stages.

"Normally we don't give pethidine late in the labour," Dr Tan said.

A lawyer representing South Western Sydney Local Health District acknowledged that aspects of the care provided at the hospital were "deficient".

As revealed by Fairfax Media, Sam and Sharon Amone were forced to deliver their own baby in the birthing suite at Fairfield Hospital because it was so understaffed.

Mr Amone broke down in tears at the inquest when he relived the loss of his baby daughter, who was named after his mother.

The baby was born with an umbilical cord tightly wrapped around her neck and had stopped breathing.

"As soon as she had the baby I just ran outside and screamed for someone to come," Mr Amone told Glebe Coroners Court.

Mr Amone told the Coronial Inquest on Monday that the baby was later gasping for air in his arms and he pressed the emergency button, but got no answer.

A registrar arrived within two minutes to remove the umbilical cord, but the father of three said it felt like "an age".

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The inquest heard that a nurse was then able to induce breathing by slapping the newborn on the buttocks, but within 15 minutes the baby was again struggling to breath.

"Her breathing seemed short, as if she was gasping for air," Mr Amone told the inquiry.

Attempts to resuscitate the baby failed.

Patrick Rooney, for the NSW government, told the inquest that paediatric and midwifery staffing levels have increased since the baby died.

Deputy State Coroner Derek Lee acknowledged the family wanted answers about why the tragedy occurred.

"No doubt your patience has been tested over the years," he said.

with AAP