Most Revd Justin Welby was addressing a gathering of inter-religious and community leaders on Tuesday evening at Lambeth Palace, where he said New Labour had also failed to come to terms with what he described as the "new issue" which comes out of society's "diversity".
Archbishop Justin appeared to suggest the pressures of modern day politics were to blame, which he said involved making "incredibly difficult decisions with too few resources, too little information and too much hurry."
However, he also praised the UK's politicians, saying they were "doing the best can" in "incredibly difficult situations" and questioned whether religious leaders from all faiths were doing enough to combat extremism.
"As the faith communities, what are we doing that provide a narrative about purpose in life and commitment to society, and benefits of a purposeful flourishing life that is so exciting that the evil temptations offered by extremists groups of all cultures and types anywhere in the world, including this country simply pale into insignificance?
"And that's a challenge for us, and let's get our house in order and then question the politicians more."
Eric Pickles, Secretary of State for Communities and Local Government, who was as the event, appeared sanguine over the Archbishops remarks. He said: "Good for him, I think the Church should be critical, I think the Church should have views because the Church should be strong, I've got no problem with that."
The Church of England recently said the UK needed a "fresh moral vision" ahead of the general election.
In a letter urging congregations to vote on 7 May, the House of Bishops said it did not endorse a political party but encouraged debate on issues such as nuclear defence and the economy.