Mrs Justice Moulder oversaw a private High Court hearing earlier this year after Premier League bosses began an investigation following allegations that Uefa’s financial fair play regulations had been breached.
She concluded that two rulings she made should be published.
But three appeal judges have dismissed City’s challenge.
Sir Geoffrey Vos, Sir Julian Flaux and Lord Justice Males have outlined detail of the case in a Court of Appeal ruling published online.
Judges explained how the Premier League had begun an investigation into City in December 2018 after saying media reports contained information suggesting breaches of Premier League rules.
They said allegations in media reports led to Uefa starting an investigation over alleged breaches of financial fair play regulations. That investigation initially led to City being banned from Uefa competitions for two years and fined 30 million euros.
The ban was subsequently overturned, and the fine reduced to 10 million euros, by a tribunal in the Court of Arbitration for Sport in July 2020.
The Premier League had sought disclosure of “certain documents and information”, begun a private arbitration process against City under Premier League rules, and an arbitration panel had been appointed.
City bosses had challenged the “jurisdiction” of the arbitrators and had subsequently asked Mrs Justice Moulder to consider the case.
Mrs Justice Moulder ruled against City after a private High Court hearing in March.
She concluded that two rulings, one relating to the merits of City’s claim and the other relating to publication, she had made should be published.
Sir Julian said, in the Court of Appeal ruling, that Mrs Justice Moulder had made “the correct evaluative assessment”, when deciding that the rulings should be published, and concluded that City’s appeal should be dismissed.
Lord Justice Males and Sir Geoffrey agreed.