The appeal follows the FA’s decision to extend the ban on fans to take in step seven clubs.
Previously the requirement for games to be played behind closed doors had only applied to steps 1-6.
Julian Rinfret, league chairman, said: “It is an understandable decision from the FA.
“It is a bit of a blow for clubs due to the financial implications, however as a league we ask that supporters stay away from matches.
“We ask fans to accept this national decision and stay away until further notice.
“The FA have asked us to do it and you can see why, we can’t kick them for it.
“The league support the FA decision. I understand people want to watch football, but please don’t put your team in jeopardy.”
The FA announcement followed a return to pre-season friendlies for clubs on August 1st which attracted fans and contravened existing guidelines.