Saturday's defeat to Chesterfield condemned John Coleman's side to a return to the fourth tier following months of battling against the drop.
"Financially, it's disastrous because I think it will probably cost in the region of half a million pounds," Dunphy told BBC Radio Manchester.
"Fortunately we've had a good season off the field with transfers and we can weather the storm."
Dunphy went on to assure fans that problems such as administration are not on the agenda for Rochdale.
He added: "We won't be going the same way as other clubs have."