Banishing faith from public life would lead to services becoming too commercialised, he said, citing as an example the suggestion that care offered by grandparents should be quantified.
He spoke of his admiration for Pope Benedict XVI, despite criticism over the lifting of excommunications of four bishops, including Briton Richard Williamson who had said he did not believe Nazis had used gas chambers to kill Jews during World War II.
Archbishop Nichols said: "What most commentators missed was that he was putting forward his action as an example of how to reach out to extremes which otherwise would be separated, would be lost and might become dangerous.
"That's a lesson for the whole of society," he said.
The archbishop said the G20 summit had been "important" and allowed nations from different backgrounds - such as China - to take their place on the world stage.
But he said: "Money in itself will never solve the problem of this financial crisis. We have to look at ways of rebuilding trust into civic life and into public life."
He paid tribute to the "robust leadership" of Cardinal Murphy-O'Connor, who he said had emerged from difficult times stronger and more buoyant than when he took on the role.
In recent years, Archbishop Nichols has been outspoken on topics like Catholic education and adoption agencies.
He has defended the way Catholic schools teach children about homosexuality, saying the Church stands "very firmly" for equal rights, and criticised government plans to force faith schools to take up to 25% of pupils from other religions.
The Vatican has made all 10 previous archbishops of Westminster cardinals.
However, Archbishop Nichols may have to wait until Cardinal Murphy-O'Connor turns 80 and no longer has the right to vote in elections for a new pope before taking the title.
The cardinal said the handover was special because the nine previous archbishops had died in office.
"I was just wondering whether I'd reach this day before emulating my predecessors," he said.
Cardinal Murphy-O'Connor said he was glad to be handing on the role to someone so "competent, compassionate and experienced".
He said Archbishop Nichols would face "huge challenges but great opportunities" in the diocese.
The archbishop is also likely to become president of the Catholic Bishops Conference of England and Wales.
He is seen as a good media performer, having commentated on the funeral of Pope John Paul II for the BBC in 2005.
In his new role, he is likely to travel on behalf of the Church and play an important role in deciding policy at the Vatican.
Kevin Flaherty, editor of the Catholic Times newspaper, said the appointment would be warmly welcomed.
"Archbishop Nichols is a dynamic churchman - a wise pastor and strong leader," he said.
"His much-needed leadership qualities will be - in the words of the late Pope John Paul II - a 'sign of contradiction' in an ever increasing secular age."
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