Despite the Scottish government's recent announcement that the festival would receive an extra Ô£2 million, doubling its current funding, Mills cautioned that the situation would remain serious.
"If you want the greatest orchestras, the greatest productions, it comes with a price tag," said Mills, indicating that budget levels are comparable to those on which it was operating at the festival's founding in 1947.
Mills, whose first Edinburgh Festival opens this Friday (August 10), also said he may exit his five-year contract early if conditions are not bettered.
"I am going to say at a certain point, 'If the festival cannot afford to put itself on for this amount of money, then it will reduce the amount it puts on.' There will be fewer nights in the Usher Hall, fewer nights in the Kings Theatre, fewer things we do. We won't be doing a different kind of show : we will absolutely be doing the same quality of work, but over less time," Mills said.