Two weeks of negotiations ended with a limited agreement that only acknowledges the need to keep average worldwide temperatures from rising by more than 2C but does not commit countries to legally binding cuts in carbon emissions.
Government representatives plan to meet again in Germany in February and in Mexico later next year to resume negotiations towards a legally binding climate agreement.
The Rev John Marsh, moderator of the general assembly of the United Reformed Church, said the failure by negotiators to agree to carbon emission cuts of 40 per cent by 2020 represented an "immense setback for rich and poor countries".
The Churches said developed countries had a moral responsibility to take the lead in agreeing a new deal to counter global warming after the expiration of the Kyoto protocol, the only existing legally binding agreement on climate change.
"History will judge our generation harshly for failing to act on the clear scientific evidence for global warming linked to human activity," said Mr Marsh. "We therefore urge the British Government to continue exerting pressure on all key players to agree the necessary cuts in emissions to reduce the risk of global temperatures rising above 2 degrees."
The Copenhagen deal was brokered at the last minute by the US, China, Brazil, India and South Africa. Even with a pledge to send developing countries $100 billion a year to help them mitigate the worst effects of climate change, developing countries were angry that the deal did not set binding targets for reducing carbon emissions.
Sudanese negotiator Lumumba Stanislus Di-Aping commented: "The promise of $100 billion will not bribe us to destroy the continent."
The Rev Graham Sparkes, head of Faith and Unity at the Baptist Union of Great Britain, said developing countries were most at risk from the effects of climate change.
"No doubt people will point the finger of blame in many different directions. But the fact is that those who will suffer most have no voice and no political power," he said.
"They are the poorest in our world, and are least equipped to deal with the catastrophic effects of climate change."
Partner of the Catholic aid agency Progressio, Fabiola Quishpe, is an indigenous farmer and community leader from rural Ecuador who attended the first week of the summit.
She said world leaders had sanctioned the continuing destruction of 'mother earth'.
She said: "The outcome means that governments will continue polluting our mother earth and we in Ecuador will continue to be affected by the changing climate."