Perry's label Capitol Records was ordered to pay $1.2 million of the damages.
"The writers of Dark Horse view the verdicts as a travesty of justice", the statement reads, according to Variety.
Flame, whose real name is Marcus Gray, was hoping for a much bigger payout - his lawyers argued that he was owed $20m (£17m) due to the stratospheric revenue Perry's fraudulent song has generated since its 2013 release.
A representative for Katy Perry was critical of Gray and his team for their estimation of the song's profits, saying: "They're not seeking fairness".
Katy Perry in a still from Dark Horse.
"We didn't try to punish anyone here", Gray's lawyer, Michael A. Kahn, said.
On the first day of trial, Perry took the stand of the witness. That included Perry, who wrote only lyrics, her co-lyricist Sarah Hudson, and Juicy J, who only provided a rap verse for the song.
The defense asserted that only fractions of the album income should be counted for the single track and that Capitol Records should subtract substantial advertising costs.
The singer reportedly made a profit of $2.4 million from the song, while Gray's attorneys argued that "Dark Horse" grossed about $41 million.
Now, the court has ruled that Perry pay a proportion of the $2.7 million settlement out of her own pocket. U.S. District Judge Christina A. Snyder, who chaired the trial, is now going to consider a motion to throw the case out.
Lepera, Perry's attorney, said outside court that the plaintiffs presented no evidence of copyright infringement, no evidence that the songwriters had access to "Joyful Noise" and no evidence the songs that were substantially similar. The only thing in common is unprotectable expression - evenly spaced "C and "B" notes - repeated".
However, that process may take months or years, as an appeal seems likely.