In the message, broadcast by the BBC, Dr Williams noted the role played by the army of volunteers in making the Olympic Games a success.
He also praised the ongoing social care provided by churches, such as the night shelters for the homeless being hosted by over 20 local churches in London.
"Religion here isn't a social problem or an old-fashioned embarrassment, it's a wellspring of energy and a source of life-giving vision for how people should be regarded and treated," he said.
Dr Williams called upon people to recognise the "steady current of generosity" underpinning many of the services in their local communities and invited people to think about what they could do.
"We should be prompted to ask the tougher question: what can I do to join this silent conspiracy of generous dedication?" he said.
"There'll be those who have time and skill and strength to offer; there¹ll be those who have less of these, but can support in prayer and goodwill."
Dr Williams preached his last sermon as Archbishop of Canterbury on Sunday.
He is succeeded by the Bishop of Durham, the Right Reverend Justin Welby, who will be enthroned in March.