Dr Carey told his congregation that while there was much pride to be taken in Britain's inheritance and the kindness of many people in society, there were also "deep pits of darkness where the light of Christ must be directed''.
In his address at Canterbury Cathedral in Kent, he said that homelessness, crime, selfishness and lack of faith were corrupting family life and personal relationships.
"All these cry out for our attention if we are seeking to reflect God's character and to follow through the demands of his justice,'' he said.
The Queen said that it was time to bring back the community spirit "which kept the flame of hope alive in the war-torn countries of Europe and the Far East during the dark days of the last war''.
Citing new-found peace in Northern Ireland, the emergence of a new South Africa free of apartheid and positive developments between nations in the Middle East, she said that a new hope had grown during the year, but it needed to be nurtured in 1995 by courage, patience and faith.
"Christ taught us to love our enemies and to do good to them that hate us.
"It is a hard lesson to learn, but this year we have seen shining examples of that generosity of spirit which alone can banish division and prejudice.''
"We can take some comfort, however, from the fact that more people throughout the world, year by year, have real hope of their children growing up in peace and free from fear,'' she said.
She remembered her visit to France for the commemoration of the 50th anniversary of the D-Day landings in Normandy in June, and looked forward to marking the anniversary of the end of the Second World War in the coming year.
She ended by paying tribute to the renowned poet of the First World War, Siegfried Sassoon, who had managed to write "amidst all the horrors of war''.
"If he could see the beauty from the trenches of Flanders, surely we can look for it in our own lives, this Christmas and in the coming year,'' she said.