The Whites failed to meet the deadline, which carries a two-division demotion.
That would mean relegated Forest Green being reprieved if City are demoted to the Southern League Premier Division.
But the decision is not expected to be ratified until the Conference meets for its Annual General Meeting on 12 June - and Salisbury have confirmed that they will appeal.
"We are not accepting the Football Conference's rules at the moment," said Salisbury chairman William Harrison-Allan.
"We are in discussions with the lawyers to see what we can do next and probably will be joining with one or two other clubs in some actions.
"I would not like to think we go down any leagues at all."
Salisbury were the Blue Square Premier's early leaders this season, only to then go into into administration, which earned them a 10-point deduction.
But they then signed a Companies Voluntary Agreement with HM Revenue and Customs in February to pay their creditors- and ended up finishing the campaign very creditably in 12th.
"The Revenue fully accepted the CVA but wouldn't take it as a one-off payment." added Harrison-Allan. "The club would have been wound up."
Forest Green manager Dave Hockaday declined to comment as the decision has not yet been ratified by the Football Association.