The Shadow Home Secretary claimed the impact of the Syrian conflict could be felt by neighbouring countries for a generation.
Ms Cooper called for fresh efforts to bring peace to Syria but warned there was no quick-fix that would see families returning to their homes in the near future.
She compared the situation to the challenge facing Europe at th end of the Second World War when the Marshall Plan was launched to rebuild the continent.
The Normanton, Pontefract and Castleford MP told the Commons: “No-one believes there is a simple foreign policy or military intervention that will restore millions of people swiftly to their homes.
“We need a serious plan to cope with the humanitarian consequences which could be with us for many years to come, a plan for the region, for Jordan Lebanon Turkey, neighbouring countries that have shown great generosity.
“But as long as the refugees have no proper homes, as long as they have no schools for children as tong as they can’t work, as long as they have no hope, of course they will seek sanctuary in European democracies.
“We will need effectively a Marshall Plan for the area, for the region, to provide the long term support that we need to provide the stablity we need.”
Ms Cooper was speaking in an urgent Commons debate she had secured on the refugee crisis where she pressed Ministers to go beyond David Cameron’s promise to accept 20,000 Syrians over the next five years.
She also questioned the Government’s insistence that refugees will only be taken from camps in and around Syria rather than those who have reached Europe.
The Government has argued that helping refugees currently in countries such as Greece would act as an incentive for others to make the hazardous journey but Ms Cooper argued thousands were taking that risk already.
The Shadow Home Secretary declined to give a figure for how many refugees Labour would accept but said it should be more than the 4,000 annually implied by the Government’s pledge and should be kept under review.
Responding for the Government, Home Secretary Theresa May told MPs that helping those in refugee camps ensured support did not just go to those fit and strong enough to reach Europe.
She said: “No-one chooses to be a refugee. The families driven out of Syria are fleeing a conflict they did nothing to start and which they have no desire to see extended.
“I know families up and down the UK listening to their stories have imagined what would we do if we were in their place, if that was our town, our home, our children.
“The awful scenes we have seen in recent weeks are all the more distressing for the knowledge they are not unique and, sadly, not new.”
Mrs May said the Government had been and would continue to do “everything it can” to help those in need of immediate aid.
She said: “Our approach is focused on four main efforts: providing aid directly to those who need it, stopping people from putting themselves in danger as they seek our help, resettling those who most need our protection and leading international efforts to bring the situation to an end as swiftly as possible.”