Orla O'Kane, who was 14, became ill last Sunday and was rushed to the Altnagelvin Hospital in Derry, where she was pronounced dead shortly afterwards.
The teenager's family is said to be particularly distressed at the delay in hearing the news because Orla's brother had now contracted the virus.
'I understand the Department of Health knew on Thursday - the parents should have been the first port of call to protect themselves and others around them,' SDLP Assembly member Pat Ramsey said.
'Clearly, the family would have handled the wake and funeral arrangements very differently if this had been confirmed in good time,' he added.
The Western Health and Social Care Trust tonight expressed its sympathy to the family of the girl.
In a statement it said: 'The Trust is reviewing the issues that have been raised to fully understand how delays occurred confirming that swine flu was present, and will agree measures to prevent similar circumstances in the future.
'Clearly these delays caused further distress for the family and that is very regrettable.'
The 14-year-old's death was the fifth related to swine flu in Northern Ireland.
A 12-year-old boy died in the Ulster Hospital at Dundonald in east Belfast earlier this month - less than 48 hours after it was announced a toddler under the age of three died.
A baby died in September but a pre-existing heart condition was determined as the cause of death.
In August the mother of two young children died. She had been fighting cancer for five years.
A soldier from Co Derry, who was based in the south of England, also contracted the virus and died in Surrey at the end of July.
