Mr Moylan told the PA news agency:
“The conflict in Israel and the Occupied Palestinian Territory has created a desperate situation with staggering humanitarian needs and intolerable suffering.
“The people of Gaza need huge amounts of humanitarian support just to meet their most basic needs. Winter will only make it harder to meet those needs.”
He said the Palestine Red Crescent Society (PRCS), which the British Red Cross works with, has so far supported more than 27,000 people as the population endures “a desperate situation and many mourn loved ones”.
Mr Moylan spoke of the lasting impact likely to be felt by those living there, saying:
“If the fighting stops tomorrow, the reconstruction and the recovery will take a decade or more.
“Mentally, people won’t ever recover in some cases.”
Calls for a ceasefire have been growing, with thousands of Palestinian lives lost in the past two months.
Mr Moylan said many donations to the Red Cross now are spent meeting people’s basic needs during a conflict such as food, water, medicine and blankets.
But he added:
“Donations also help us support people dealing with the trauma of losing loved ones and homes during disasters and conflict.
“This psychological support means we’re there for people in the worst moments of their lives and allows us to help people as they slowly try to recover from disasters and conflicts.”
He added:
“Conflicts and disasters will undoubtedly have ongoing, long-term psychological impact on people and especially children across the world. These impacts will be felt long after our attention in the UK has shifted to other crises.