The health minister told the Northern Ireland Assembly that he had been made aware of 20 cases in which the trust's response was said to be below standard.
The patients were seen in the emergency, obstetrics, gynaecology or X ray departments.
It is not clear whether the deaths were avoidable. Edwin Poots said the trust's response should have been better.
He said this was especially true, where cases were not identified as "serious adverse incidents".
It is understood the babies were either born prematurely or were less than a month old.
The trust is also completing a review of about 35,000 X rays taken at the Causeway Hospital, Coleraine, County Londonderry, between 2011 and 2012.
Nine patients have been recalled. That review is now being extended across the entire health trust, involving 48,000 X rays.
Health Minister Edwin Poots said the cases, which date from 2008 until the present, were discovered by a "turnaround team" he had sent to the trust.
"I wasn't happy with the Northern Trust, I wasn't happy with the way things were being done there and that's why I put a turnaround team in," he said.
"We do need to offset that  with the fact that the Northern Trust was dealing with tens of thousands of cases.
"The Northern Trust is in a considerably better place than when I inherited it in 2011."
Mr Poots said Northern Ireland's hospitals "are safe places", but added: "Do we run perfect hospitals? We don't."
Maeve McLaughlin, the chair of the assembly's health committee, said the the news of the cases was "quite alarming".
"I think there are very serious questions [to answer]," she said.
In a statement, the trust said it recognised that on certain occasions it had "fallen short of the standards the public should expect from us".
"More critically, we failed to learn from these incidents. To those people affected we apologise," the statement said.
"We have identified 20 separate incidents over a five-year period where the response by the trust was below standard. We have advised the department and welcome the minster's statement today and his continued support."
The statement said patients and their families had been let down.
It said it would work to try and prevent that happening in the future and was committed to "a culture of openness and transparency".
The trust said that changing the culture was the key to turning the organisation around.
The deaths of five babies are among 11 under investigation at the Northern Health Trust.