Epic has launched an appeal against last week's ruling in its case against Apple's App Store policies.
On Friday, the court issued a permanent injunction stopping Apple preventing app developers from directing users to payment methods outside the App Store - seen by many as a loss for Apple.
But the court also ruled against Epic on nine out of 10 issues and ordered it to pay millions of dollars in costs.
Epic boss Tim Sweeney said he was "as determined as ever to fight on".
Epic had argued Apple's tight control of its iOS platform amounted to a monopoly.
But the court found Epic had failed to prove its case.
"The court cannot ultimately conclude that Apple is a monopolist," judge Yvonne Gonzalez-Rogers said.
Apple has characterised the ruling as a clear win, saying it is about communication between app developers and users.
But the injunction allowing developers to link to their own purchasing mechanisms - the only part of the ruling to have gone against Apple - may mean fewer customers use Apple's in-app payment systems, which take a 30% cut.
The court has given Apple a 90-day grace period before the ruling takes effect
And the technology giant has yet to decide whether to appeal.
It also remains unclear whether any change would be limited to the US market or rolled out worldwide.
Today: Lost a court case, climbed a mountain, read hundreds of pages of legal papers, wrote some code. Just as determined as ever to fight on until there is genuine developer and consumer freedom in software, and fair competition in each mobile platform software component. pic.twitter.com/5PWD6va6mz— Tim Sweeney (@TimSweeneyEpic) September 11, 2021
In the wake of the ruling, Mr Sweeney tweeted: "Today's ruling isn't a win for developers or for consumers.
"Epic is fighting for fair competition among in-app payment methods and app stores, for a billion consumers."
In a filing Sunday with a California district court, Epic gave notice to appeal against the judgement - "and all orders leading" to it - but without much further detail.
A similar court case between Epic and Google, which runs the equivalent Android app store, continues.