Speaking in the wake of the massacre of 26 schoolchildren and teachers in the US earlier this month, Dr Williams said stricter controls over the sales of weapons would be only “a start”.
“But what will really make the difference is dealing with fear and the pressure to release our anxiety and tension at the expense of others,” he added.
In his final Christmas message as the Bishop of Durham, Bishop Welby, who will formally take over from Dr Williams in March, said next year would be a personally “momentous” period.
Addressing the challenges he faces as the 105th Archbishop of Canterbury he said he “did not seek” his new role but pledged to do everything in his power to “make a difference” to the Church of England and the country at large.
“The Church gets lots of things wrong, it always has, always will, because it is full of human beings,” he said. “But at its heart is the good news that when Jesus came God came to be with us, offer us hope and joy and purpose and love beyond all we can measure. That keeps me going.”
Emphasising the importance of combining festivities with a sense of “responsibility” to others, the former oil executive said: “In tough times like these, it can sometimes be difficult to focus on the positive; talk of recession, news of redundancies and reports of worldwide conflict grinds us down. However, Christmas is a time for celebration, it always has been.
“The shepherds, poor as you could be even in those days, went to celebrate what had happened in a manger, where they found God Himself.
“Christmas also brings with it the risk of so clubbing ourselves round the head with spending and parties that we forget who we are and why we live.
“At the heart of the greatest story ever told, the Christian story, the story that has shaped our civilisation, is the theme of self-giving and responsibility.”
He added: “The best parties have something solid to celebrate, not just a desire to get out of one’s mind.
“The shepherds went to see Jesus and went away celebrating because God had come to be with them. They were optimistic. Hope lived. And hope and joy are better when shared, in fact sharing them makes them grow and gives them life.
“So, my own sense this Christmas is one of optimism. I see people staffing food banks, sharing good things, sacrificing to give.
“Perhaps just going to see a neighbour, hurrying a bit less when someone wants to chat, we can all do that. Perhaps we can give something to someone who has had a rough year, make space for them to have hope and joy.”
In a Christmas message to Sunday Telegraph readers Dr Sentamu said: “When so many are struggling in our society during this economic downturn, what we must ask is: do we want to live in a country where inequality and suffering is ingrained, or would we rather send out a message of the Christian virtue of hope – that everyone is valued and has an important part to play.
“This Christmas as we remember the great joy and hope brought by the birth of God’s son, Jesus Christ, let us remember our responsibility to love and care for our neighbour, especially those whose needs are greater than our own.”
Dr Sentamu’s message came after he issued a warning against the Government’s “severe” defence cuts, saying they needed to be carried out with “far, far greater sensitivity”.
Meanwhile Cardinal Cormac Murphy-O’Connor said: “St Leo calls Christ’s birth ‘life’s birthday’ because if God is with us, then in a mysterious but real way, we are all brothers and sisters to God made man. It is in gazing on him that we see our own true worth.”
He added: “The light which came into the world at Bethlehem, the love which that tiny infant embodies is a light and a power for all of us to live by as we strive to create a better world, each in our own way.”