The vaccination programme is to be extended in the coming weeks
The swine flu outbreak has led to the Department of Health facing the "most difficult winter" in many years.
Senior health officials made the remark during an emergency meeting with the Stormont health committee.
However, committee chairman Jim Wells said he felt "a lot more reassured" after the meeting that the department was "on top of the difficulty".
A swine flu vaccination programme for children with complex special needs began on Thursday.
It comes after three more people in Northern Ireland died from illnesses related to the H1N1 virus on Wednesday.
Two of the victims are understood to be children who attended special schools and the third a 62-year-old man.
Mr Wells said he was "very impressed" that the Department of Health had rolled out the vaccination programme "so quickly" to 40 special schools.
He said that 2,500 special needs pupils who have underlying health problems would be given protection against the virus by Friday.
But he said he was disappointed that department was not prepared to include teaching staff at special schools in the swine flu vaccination programme and he urged health officials to reconsider this decision as a matter of urgency.
Preparations have been in place to vaccinate children with special needs
The chairman said he was relieved that the predicted number of swine flu-related deaths in the UK had been revised down to 1,000 but added that there was "a lot of work ahead" to bring the situation under control.
In its latest update, the Department of Health said there were 146 new laboratory confirmed cases of swine flu in Northern Ireland, up 23% on the week before.
The total number of confirmed cases since the beginning of the outbreak now stands at 663.
In a separate meeting on Thursday, senior education officials met the Public Health Agency to plan how schools should deal with swine flu.
Schools will also be provided with a draft letter to issue to parents to reinforce the Public Health Agency advice.
They were also advised to remain vigilant for signs of flu-like symptoms.
PHA advice is that as long as children are well and not suffering flu-like symptoms there is no reason to stay away from school.
On Wednesday, a second child from Foyleview special school in Londonderry, Ashleigh Lynch, died after contracting swine flu.
Ashleigh's fellow pupil, 14-year-old Orla O'Kane, died last week.
Ashleigh was one of three people to die on Wednesday after contracting the virus.
The health department said a 62-year-old man with swine flu had died but "it was not the cause of his death".
A third patient with swine flu and other complex health issues has also died in hospital.
No further details were released, but it is understood the victim was a young child who attended a special school in Belfast and had been in intensive care.
Preparations for the vaccination programme in special schools were already in place before these latest deaths.
Foyleview special school principal Michael Dobbins said they had not been advised to close the school, despite the deaths of two pupils.
"Special schools are a hub for a range of services for children with special needs - they receive a range of therapies which in some cases are central for maintaining their conditions and enhancing their lives," he said.
"Our focus is about being there for our children and families - I haven't had one phonecall from a parent suggesting we close. In fact it's been the opposite.
"The last thing we want to do is close, but if we get medical advice suggesting we close, we will take it."
He added: "Ashleigh and Orla brought so much to the lives of their families and to us as a school - it's heartbreaking."
His counterpart at a special school in Dundonald, east Belfast, called for all staff and pupils at special schools to tested for swine flu.
Tor Bank principal Colm Davis said it would "give staff and parents a level of reassurance".
Ten people from Northern Ireland who had the virus have died - eight in NI and the other two in England and Spain.