The letter was sent home with pupils across the city on Tuesday.
It warns of a “crisis in education” and of cuts to staff numbers, increased class sizes and longer waiting lists for special educational needs services.
School heads also urge the North’s politicians to return to government.
In the letter, principals from across the Catholic, controlled, integrated and Irish medium sectors, said: “As educationalists we have always been proud of the high standards that we have been able to deliver in all of our schools in Derry throughout the year.
“However, all of this is being compromised and threatened by the lack of financial and political support that we are being given to run our schools.”
The principals said the amount of funding received per pupil has been cut by 4% over the past four years.
Parents were told that reduced funding may mean cuts to teaching and support staff, longer waiting lists for additional and special educational needs services and higher charges for after-school clubs are “an inevitable outcome”.
Swimming lessons, music tuition and school trips could become unaffordable, according to the head teachers.
They also urge all parents to lobby politicians and state other areas of the UK have significantly better funding for education.
The North of Ireland has been without a devolved government since January 2017 when the Assembly collapsed in a row over a botched green energy scheme.
The letter concludes: “We need the amount of money that we received for each child to be restored, at least, to its original value to assist us in delivering high quality education to our children.”
SDLP leader and Foyle MLA Colum Eastwood said: “This letter should be enough to inject a sense of urgency into our process.
“It is a total disgrace that we still have no government.
“And no attempt is being made to sort the problem out. Our children are suffering because our politics is broken.”
Foyle Sinn Féin MLA Karen Mullan said she was “fully supportive of the request for greater funding to go to education”.
“The restoration of the assembly and executive will not of themselves address the funding issues facing education.”
“That can and will only be done when the British Government abandons its austerity agenda and restores the block grant to the levels that address the needs of the people of the north,” she added.
Mayor of Derry John Boyle said there was an onus on politicians to listen to the principals’ concern and he was looking at possibly setting up meetings “to address what are very real and worrying issues for local parents and school principals”.