The lawmakers' report argued that preventative work with communities, families and international partners is vital and needs to be a top priority for the UK Home Office.
Vaz, who is chairman of the House of Commons Home Affairs Select Committee, said, "The number of cases being brought to public attention should ring alarm bells. This must be a relentless battle for hearts and minds, and without a strong counter-narrative we are in danger of failing to prevent even more departures. We are at the edge of a cliff."
After taking evidence from the police and the families of the three girls among others, Vaz said their case suffered from a "lack of immediate action".
He added: "Schools and the police must inform parents immediately, and work with them even if there is the smallest hint of radicalisation, or a close association with someone who is thought to have been radicalised."
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He said the committee's criticism was "misleading", pointing to the evidence given by both UK and Turkish authorities of "rapid exchanges" between the two.
The committee's report said there needed to be an advice service which would be a less extreme step than calling the anti-terrorist hotline.
The Association of Chief Police Officer's lead officer for the government's anti-terror strategy Prevent, Chief Constable Sir Peter Fahy, agreed that more needed to be done.
However, he said the police "do not have the capacity" to routinely work with every school in the country.
The committee also pointed to weaknesses in information sharing with airlines and other countries.
It said greater care needed to be taken at airport check-in desks when people were travelling to destinations of concern - namely Syria, Somalia, Iraq and Nigeria, as well as neighbouring countries, such as Turkey.