"We don't want to point the finger at people just so they feel guilty, but we need to remind them there are moral values worth espousing," Dr George Carey, 61, said in an interview in the Easter edition of the Radio Times.
"Shame is a very important and neglected word. They may cohabit and in some cases it may be virtually the same as marriage. I want to ask them in that case why not marry? My fear is that cohabitation will bring down the institution of marriage."
The Archbishop said that the country had a great debt to Christian teachings but this was now in danger of being lost with "do-it yourself" relationships.
"If you take that kind of attitude, you form liaisons with whom you choose, but you have responsibilities to each other, to the community and to your children," Dr Carey said.
The interview comes ahead of a three part BBC documentary series beginning on Sunday, 6 April, entitled Archbishop - A Year in the Life of George Carey.
His forthright views on marriage will we welcomed by critics who claim he has in the past prevaricated over important moral issues.
"I've never believed leadership means sitting on fences. I'm not wishy- washy. I have clear goals but life is complex," said Dr Carey.
"You can still give a moral lead but it is unwise to say everything is black and white. Where there are shades of grey we must paint the picture as it is."
In the interview, Dr Carey admits divorce is not a "black and white issue" even in the Bible and that while homosexuality is a sin, he wants gays to "feel loved by Almighty God".
On politics he admits to reservations over the excesses of the 1980s.
"The Thatcher era gave us the feeling we can do things, take responsibility for ourselves and that was a very good message. But there are those who need extra help," he said.
"Politics is too important to be left to politicians and religion is too important to be left to clerics."
He did not believe Parliament was ready to sanction the disestablishment of the Church of England and declared himself "ready and relaxed" on the constitutional issues ahead.Reuse content