He's made the comments in a radio interview broadcast today, as he continues a six-day tour of the Middle East.
The Prince of Wales has also spoken of about wanting to 'build bridges' between people of different faiths.
He said it was particularly concerning "in a country like ours where you know the values we hold dear".
"You think that the people who have come here, born here, go to school here, would abide by those values and outlooks," the Prince told BBC Radio 2's The Sunday Hour.
The Prince of Wales landed in Jordan late on Saturday, where he is due to hold talks with Jordan's King Abdullah II.
Jordan has carried out three consecutive days of airstrikes on Islamic State targets after the terrorist group released a video showing 26-year-old Jordanian pilot Moaz al Kasabeh being burned to death.
Prince Charles said preventing the radicalisation of Muslim youth was a "great challenge" and something that could not be swept "under the carpet".
He also expressed particular concern over the threat posed by young Muslims coming into contact with extremists online, describing it as "frightening".
"I can see I suppose to a certain extent, some aspect of this radicalisation is a search for adventure and excitement at a particular age," he said, adding that he had tried to create alternative paths for young people through his work with The Princes Trust charity.
Charles also suggested that when he becomes King he may still be sworn in as Defender of the (Anglican) Faith, despite speculation that the title could be changed to encompass all faiths.
But he said he believed an important part of the role was to be a "protector" of every religion in multicultural Britain.
As heir to the throne, Charles is also heir to the title of Defender of the (Anglican) Faith.
He said: "I said I would rather be seen as defender of Faith all those years ago because... I mind about the inclusion of other people's faiths and their freedom to worship in this country.
"And it always seems to me that while at the same time being defender of the faith you can also be protector of faiths.
"You have to come from your own Christian standpoint, you know, in the case I have defender of the faith and ensuring that other people's faiths can also be practiced."
The Prince's tour will see him travel to Kuwait, Saudi Arabia, Qatar and the United Arab Emirates.
