Hearts and Partick Thistle have released a joint statement admitting their disappointment at the outcome of the arbitration decision.
The two clubs revealed they have been asked not to share details of the hearings on confidentiality grounds but they did say they don't regret going down the route they did.
And they've also reiterated their blame that the SPFL have put the entire burden of the COVID-19 pandemic on three clubs.
Stranraer were also relegated from League One but didn't take part in the court battle, with financial implications believed to be the reason.
But Thistle and Hearts were both willing to go all the way and took it to Edinburgh's Court of Session. It was then decided that their battle with the league governing body would be decided by an arbitration panel, hosted by the SFA.
They lost that fight earlier on Monday and they said: “As all parties have been requested not to comment on the tribunal’s decision or reveal details of the hearings on the grounds of confidentiality, all we can only say is how disappointed and surprised we are at the outcome.
“We don’t regret taking this action as it was the right thing for us to do. There were better ways to deal with ending the season, fairer ways other than putting the burden of a pandemic on to three clubs.”
The two clubs now face a separate SFA hearing after being hit with notices of complaint over their decision to go to court.
And SPFL chief Neil Doncaster claimed it as a huge victory when he said: "This is a clear, comprehensive and unanimous decision.
“I am absolutely delighted that our approach has been vindicated throughout, following an intense period of legal scrutiny and review.
“It has been a very demanding process, but I had complete confidence in the actions and decisions of the SPFL board and the SPFL executive team.”
