The number of Christians in Aleppo has fallen more than 200,000 to less than 35,000 over the last five years.
Sister Annie Demerjian told MPs many families were living without basic resources including food, heating and light and each day brought a new struggle for clean water and fuel.
Speaking at London's Houses of Parliament, she said: "People in Aleppo are tired.
"There is a lack of basic essentials - water, medicine, food and fuel shortages. Aleppo is a broken city with death, destruction and violence".
She described how "many people were without light", as they could not afford electricity in Aleppo, because of the "exploitations by traders".
Sister Annie went on to say that such shortages mean that "thousands of families are without fuel - facing this winter without heating".
Reflecting on attacks on the Church, Sister Demerjian said that people are worried.
She said: "Everyone is afraid - we lost people we knew. The Church community has become so small that we all know each other".
Supported by Archbishop Shaw of Lahore, the pair called for religions to listen to and respect each other, hoping that "all religions can work together for peace".
By Dan Golding