He admitted that there was a "pressing need" to equip the Church "confidently to discharge that calling" in the face of the economic uncertainty, high levels of unemployment, the widening gap between rich and poor, and cuts in public spending.
The Archbishop spoke of the need to "assert the value and importance of the contribution of trust in God to our national life".
"Of course, religious faith can be a source of division in society, but so can many other differences in human understanding and allegiance," he said.
"The fact is that all our communities benefit from the contribution of those who adhere to the worship of God, expressed in a life of service to their fellow human beings."
Dr Sentamu went on to say that the Church of England had a responsibility to build up the "wellsprings of solidarity" in British society and defended it against the attempts of critics to confine the church to the private sphere.
"We must actively continue to seek to influence the terms of the national debate on key issues affecting our society," he said.
"Morality is or should be increasingly a matter of public concern and not just a private matter."
He continued: "As we try to re-articulate, in today's circumstances, how the moral order should be reflected in the compact underlying our society, we cannot expect to be universally welcomed or applauded.
"But to do these things is, quite simply, our God-given duty and our particular calling."