Rick Parry fears Bury may not be the last EFL club to lose their membership over financial difficulties.
The Shakers were expelled from the league in August after failing to provide financial guarantees to the EFL, with a late takeover bid also collapsing.
League Two club Macclesfield are in a perilous state, having been charged in November with misconduct by the EFL over failing to pay players' wages. The Silkmen also face further disciplinary action after the club failed to fulfil their fixture against Crewe last weekend.
Parry admits it is unlikely Bury will be an isolated case.
"I definitely can't say (Bury) will be the last, there may be more fall-out to come," he said.
"We have seen the problems with Macclesfield which are fairly extreme and they are not the only one. Maybe we are going to have to go through more pain before it gets better."
Parry did not feel the issue was that there were too many clubs in the EFL structure.
"I don't think we have got too many clubs, there are many full-time clubs thriving below the EFL," he said.
"There are a few bad owners and maybe there are still a few to weed out."
The problems faced by Bury will be addressed as part of an independent review of EFL governance by Jonathan Taylor QC, a barrister specialising in sports law.
One solution may be the introduction of clearer, tighter salary cap rules.
Parry admits the decision in rugby union to dock Saracens 35 points for salary cap breaches suggests such sanctions are legally enforceable and that it is an area which could be explored.
"The Saracens decision says it must be lawful because it is something they have enforced," he said.
"We always felt it was something that couldn't be explored. I've heard clubs recently say maybe what we have is too complex and maybe we should concentrate on the issue we are all concerned about which is wage costs and focus on something similar.
"But to say that's the majority view or something that is likely to happen is way off the mark. It's part of the debate.
"We do have quite different rules in Championship compared with salary cost management protocols lower down. That works, but some clubs think we should have more of an alignment and one set of rules."
