Justin Welby also said reasons for war and violence must be strongly challenged and carefully thought through before they are used as a justification.
He added that Christian and Muslim leaders must "up their game" and speak out against extremism in Iraq and Syria.
Islamic State has forced thousands of people to flee their homes as they threaten Christians with death.
Archbishop Welby wrote in Prospect magazine that the war against IS is "a terrible mix of ethnicity, economics, social unrest, injustice between rich and poor, limited access to resources, historic hatreds, post-colonial conflict and more - which need to be tackled ideologically".
He added: "The victory requires us to reshape our values, as much as to overcome those of IS."
The Church of England leader also said persecution of Christians, other religions and ethnic minorities was becoming much more severe.
The United States has carried out 21 air strikes over the last two days to aid Syrian Kurdish forces on the ground.