The government is encouraging more faith schools to be set up in England and the Church wants to create at least 100 more secondary schools.
But the whole issue became more contentious than ever with the riots in northern England during the summer.
Reports on the disturbances pointed to single faith schools as being something which had heightened racial divisions.
Popularity 'problem'
Interviewed on the Today programme on BBC Radio 4, Dr Carey said the country had a long history of faith schools, which of course required people to have a commitment to a faith.
"But I want to remind you that - in the case of the Church of England - we include anybody in that neighbourhood. If they want to come we are glad to welcome them.
"Indeed part of the problem is that we're so popular we want to have more schools so that we can actually do our job properly and include as many people as possible.
"We are here, we are making a very distinguished contribution to education in our country, we want to continue that, we want to deepen it, but we want to deepen it not at the price of exclusion. We want to include people."
In many urban areas in particular, a lot of Muslims and children of other faiths attended Church schools, he said.
Stress on inclusiveness
The Cantle report on the riots said that the existence of schools dominated by one race or faith - not necessarily faith schools as such - had contributed to racial tensions.
It proposed that any such schools - including independent schools - should have to offer "at least 25% of places to reflect the other cultures or ethnicities within the local area."
There are about 70 independent Muslim schools which, not being part of the state system, do not have to teach the national curriculum.
Dr Carey said: "We want inclusion. As long as faith schools are signed up to the national curriculum, are inclusive, they can make a tremendous contribution to our nation."
Alternatives
At present, religious organisations contribute 15% to the capital costs of state schools they control. The government's plan is to cut that to 10% - with the rest coming from public funding.
The Local Government Association has "deep reservations".
It would like faith schools to take no less than 75% of their pupils from other religions or no religion.
The British Humanist Association has proposed a series of measures, such as flexibility on school uniforms and meals, which it argues would make all schools fully inclusive and remove the need for faith schools.
It believes that its proposals "will be opposed only by tiny minorities determined to segregate their young people or to proselytise at public expense" - objections which it says should be discounted in the interest of social cohesion and good education for all.
The National Secular Society argues that religious tension will only be exacerbated by the creation of more faith schools.
It wants religious criteria to be banned from the entry requirements of any publicly-funded school and in the longer term, faith schools be transferred to the community sector.