Lana Ameen died in hospital just two days after she apparently caught a cold and then had a high temperature.
Her mother, who is a nurse, and father, a doctor, want the British government to ensure the H1N1 vaccine is available to everyone, in particular children.
Lana became ill on Christmas Eve. Gemma Ameen and her husband, Zana, initially took their daughter to Stepping Hill Hospital, Stockport, Greater Manchester where she was diagnosed with an infection and sent home.
Later the same day she was rushed back to the hospital after she suffered multiple fits. The couple from Quinton, Birmingham, claim she then had to be revived three times as they say a junior doctor refused to call a specialist consultant.
Lana was eventually transferred to Alder Hey Hospital in Liverpool but died the next day.
Speaking to the Manchester Evening News, Ms Ameen, 28, said: “I want to say to people, to parents, if you can get the vaccine don’t hesitate — the risk of not having it and the price you might pay is just too high.
“We have been so shocked by what has happened and we feel very strongly that everyone, particularly children, should have the vaccine.
“Even financially, surely it makes sense. The swine flu vaccine is inexpensive and has already been bought — it cost £1,700 (€2,000) just to care for Lana in intensive care for one day.”
Bosses at Stepping Hill have launched an investigation into the girl’s treatment.
Dr Chris Burke, chief executive of Stockport NHS Foundation Trust, said: “To date, that [case] review has identified that Lana received appropriate treatment and care in a timely fashion.
“In spite of our interventions, Lana’s health continued to deteriorate until her death at Alder Hey.
“We will extend an invitation to the family to meet with senior clinical staff to discuss the treatment provided to Lana and their obvious concerns.”
Last month, a five-week- old boy who became critically ill with swine flu was earlier sent home from the same hospital with indigestion medicine.
The parents of Harvey Flanagan decided to take him to another hospital where the virus was revealed and he later recovered.