Clubs were assessed on league performances, attendances, facilities and provision for women's and youth football.
"The club wishes to acknowledge the overwhelming reaction of support from its members; coaches, players of our 14 teams, supporters, politicians and community representatives," added the Donegal Celtic statement.
On Wednesday, Donegal Celtic manager Paddy Kelly confirmed that the club would appeal against the decision.
"We'll certainly appeal on the points systems and the grading," said Kelly.
The Donegal Celtic boss indicated that legal action is likely if their initial appeal is unsuccessful.
"We would like to know how clubs got above us and how we lost points.
"If we don't agree with that, I dare say we'll be taking legal action."