The petition, launched by the family of two-year-old Faye Burdett, who died in February from Meningitis B, called for the vaccination to be extended to children up to the age of 11. It currently has 823,346 signatures.
However, experts from the Joint Committee on Vaccination and Immunisation (JCVI) said that extending the jabs to older children would not be 'cost effective'.
The Bexsero vaccine is available on the NHS for babies aged two months, followed by a second dose at four months and a booster at 12 months.
Parents with children older than a year would have to pay privately to get their children vaccinated. Prices are rising to £750 because of low supplies of the vaccination. However, Boots recently said they had stocks of the vaccine back in, which cost £95.
The report from the JCVI meeting in June said: 'The committee noted there was unlikely to be any vaccine available to deliver any programme to those aged 12 to 23 months of age before the 2016/17 meningococcal season.
'The committee were also concerned about the serious risks to the infant programme that the use of Public Health England's buffer stock could present. Given these concerns, the committee agreed that they could not advise the Department of Health to consider such a catch-up programme.'
In February Rugby player Matt Dawson spoke out about how he and his wife went through 'two weeks of hell' when their son, Sam, was struck down with the disease. He took to Twitter to urge people to sign the petition.
Liz Brown, chief executive of Meningitis Now, said: 'We are hugely dismayed by today's decision, but will continue to campaign passionately for all children under the age of five to receive this lifesaving vaccine.
'We stand for the many thousands of families who are unable to protect their children from this devastating disease because they cannot afford to buy the vaccine privately.
Professor Andrew Pollard, JCVI chairman, stands by the decision: 'The JCVI continually reviews vaccination programmes - including men B - and considers changes based on current scientific evidence. At our latest meeting, the committee concluded that a catch-up programme for older children cannot currently be advised.
'Offering a catch-up programme to children aged one to two years could be cost effective, but doing so could put the routine programme - and those babies with the highest rate of disease - at risk.'