There is less chance of schools detecting that pupils are being radicalised if parents do not know it is happening, Tristram Hunt has said.
More and more responsibility is being put on to schools and teachers, according to the shadow education secretary.
He suggested that other public services, like social work, have been "stripped away" leaving schools with more to take on.
Education Secretary Nicky Morgan said all of society needs to be aware of the signs of radicalisation, adding that it can happen outside the school gates.
The comments come after it was disclosed that three schoolgirls flew to Syria to join Islamic State (IS). The teenagers, who attended Bethnal Green Academy in east London, flew from Gatwick to Istanbul on February 17 and are feared to have continued on to Syria to become so-called "jihadi brides" with IS militants.
At a TES pre-election debate with politicians from the three main parties, it was suggested that there is a need to be realistic about what schools can do to stop pupils being radicalised.
Mr Hunt said: "On radicalisation and the situation in Bethnal Green, I think this is really difficult because I think culturally, we're putting more and more on teachers and on to schools. If the parents themselves didn't know what was taking place, the chances of the teachers and the head teachers themselves knowing was more challenging."
IS and radical Islam is a "poisonous and cancerous ideology" which is capturing the minds of some young people, he said.
The Labour politician suggested that schools are "one part of the public realm which have suffered not so badly as other parts in the last few years".
"Once you see the stripping away of youth work services, the stripping away of social workers, the stripping away of all those other elements of the public realm which do play a role in the safety and security and happiness of our young people, we end up having more and more challenge on schools with directives from the Secretary of State to the schools, and I think we have to be realistic about what schools can and can't achieve."
This does not mean that they should not teach core values like tolerance, Mr Hunt said.
Mrs Morgan told the election hustings: "I've spoken to the head at Bethnal Green, he is very convinced that they have done a lot of work within the school on this potential issue, but there is of course always more that can be done.
"I think we are all now much more aware of the dangers to our young people but I think we are also right to highlight that a lot of the radicalisation can happen outside the school environments, the influences of the internet and others, community groups, so I think it's incumbent on all of us who are working with young people to watch out for the signs but I think we are much more alive to it."
The Conservative Secretary of State said it was important to talk about "core common values" adding that there was a lot of work going on that she was unable to discuss, that is tied in to "stopping young people from being groomed on the internet to then travel abroad to a dangerous situation, which is what I think happened here".
Lib Dem schools minister David Laws said that the biggest force against radicalisation is education.
"An educated young person and an educated population has to be far less likely to go down routes of barbarism that we've seen on our TV screens and in the media over the last few months and therefore the need to challenge radicalisation takes us back to all of the things that we've been talking about in relation to good education.
"But I fear that we have to say this too, that it's not just good education any more, but it's also being aware of the risks in particular communities."
Mr Laws said it was a "sad truth" in society today that schools in areas where there is a risk of radicalisation "need to be acutely conscious of the risks inside the school gate and outside".