Alliance proposed the debate and urged John O'Dowd "to prevent a repeat of the problems being faced this year".
Mr O'Dowd has already agreed to remove the criteria which gives priority to children born in July or August.
But Alliance MLA Judith Cochrane said the change must be in place by June in order to take effect in 2013/14.
She said the move would require an amendment in legislation.
Ms Cochrane said she had called the debate in order to put pressure on the minister to take immediate action, so children enrolling next year would not be adversely affected.
The UUP has also claimed that the current system of allocating funded pre-school places is not working.
UUP MLA Jo-Anne Dobson said there were "big financial implications" for the parents of children denied a place.
Ms Dobson, who represents the UUP on the assembly's education committee, said the matter was at the forefront of many parents' minds.
"The unmet need for funded nursery places is having a devastating effect on parents every year and the damage caused will show on our young children for generations to come," she said.
In January, Mr O'Dowd announced a number of changes to the way in which funded places would be allocated in future.
He confirmed that children born in July or August would no longer get priority and he promised to review and broaden the definition of social disadvantage.
The system of giving preference to families in receipt of benefits was also to be re-assessed.
The minister's announcement followed a review of pre-school admissions arrangements, carried out by the Department of Education.