According to the Church Times, the Most Rev Justin Welby said that those who voted to stay in the EU needed to consider the rights of "democracy" and focus on "reuniting the country."
Speaking at a question and answer session at the Christian festival Greenbelt, Welby said: "We have to take seriously the fact that the majority voted Leave.
"We may not like it, but that is democracy; and that means we have to stop whingeing about it and do something about reuniting the country."
He said he was a "democrat" who did not support the campaign for a second vote.
He warned that the country must come together behind a "vision for this country that is outward-looking, is done top-down, middle-out and bottom-up" and suggested the Church of England could help to ease tensions between Leavers and Remainers.
"'The Church is one of those institutions that can do that," he added.
The Archbishop's comments follow reports last week that he is in talks to chair public meetings to discuss how a no-deal Brexit can be avoided.
He has been approached by a cross-party group of senior MPs, including Christian Conservative Dame Caroline Spelman.
The forum is due to take place at Coventry Cathedral next month.
The Archbishop has insisted that any forum should not be a 'Trojan Horse' for cancelling Brexit and has received support from his fellow clergymen, the Bishop of Buckingham.
The Right Rev Alan Wilson told Premier: "When I first heard of it I thought this is quite a good idea because Coventry Cathedral is involved and we know that they have real strength in reconciliation.
"There is a Christian mandate from Jesus about loving our neighbour as ourselves and that means a concern that the best possible outcome comes from all this for everybody."
Some have criticised the move saying the archbishop should not be getting involved in politics.
Sir Gerald Howarth, former Conservative MP, Brexiteer and Christian, told Premier: "This is a very sensitive political issue and I know the Archbishop reasonably well, he's a very intelligent man, but I think that he is treading on very thin ice here if he's going to get involved in this very tortuous business."
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