Relegated Stranraer are "disappointed" in the outcome of the SPFL's vote to end the season, but say it would be "very expensive" to challenge.
Partick Thistle, who will be relegated from the Championship, sought legal opinion which indicated grounds for dispute.
But Stranraer chairman Iain Dougan says its not an option for them as they drop into League Two.
"Legal actions are very expensive," he said.
"We're one of the Scottish minnows. Ultimately any legal challenge against the SPFL and the organisation, which is all 42 clubs, if defended, it's the clubs that pay to defend it."
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A taskforce, led by Ann Budge of Hearts and Les Gray of Hamilton Academical, will discuss league reconstruction for next season.
Dougan says getting clubs to agree to a reshuffle of the leagues is a "very, very hard task".
"She's [Budge] got the unenviable task of trying to come up with a plan for reconstruction that would appease most and have the least resistance, not only saving themselves but not being detrimental to other clubs," he said.
On Wednesday night, Falkirk said they would "reluctantly accept the outcome" of the vote, which denied them the chance to win the Scottish League One title.
They trailed Raith Rovers by a point, but had a far superior goal difference, when the leagues paused on 13 March.
Falkirk voted against the SPFL's plans last week and are "disappointed" that Dundee's late U-turn proved decisive.
However, they have welcomed the news that the suggested expansion of the top flight could mean being elevated to the Championship with Raith.
"The impact of the pandemic on Scottish football could and should have been handled better," read a statement.
"It is now vital that league reconstruction takes place as soon as possible. We will, of course, contribute positively.
"It is our strong belief that urgent and meaningful league reconstruction is essential given the disruption caused by the early ending of the season and the unfair consequences for many clubs, Falkirk included."