Partick Thistle finished bottom of the SPL
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Partick Thistle will not contest the SFA's decision not to hear their appeal against relegation from the SPL.
The SFA's said on Thursday night that they had no jurisdiction to rule on the SPL's decision to promote Inverness.
A club statement read: "Although there are other legal options available these would be time consuming and incur further expense.
"First and foremost we are a football club and all our energies will now be channelled in that direction."
The 12 top-flight clubs voted last month to allow promotion to Inverness Caledonian Thistle, who will ground share with Aberdeen next season.
But the Jags, who finished bottom of the SPL, decided to appeal to the SFA.
However, the SFA's Appeals Committee ruled that the SPL's voting procedure was not "imposed" on Partick Thistle and therefore the issue was not covered by the governing body's articles.
The Partick statement continued: "The legal steps taken by this club were always with a tacit acceptance that the SFA was the ultimate authority in Scottish football and with the aim of achieving an independent interpretation of Rule A2.3.1. of the Rules of the Scottish Premier League.
"The Board now accepts that this will not be possible."
Inverness failed to get the required 8-4 majority to approve a ground-sharing scheme with Aberdeen when the 12 clubs first met to decide the issue.
But a second vote resulted in a 10-2 majority in favour of Inverness' plans.