Justice Robert Bromwich said a payment of $150,000 in damages should sufficiently meet the "sting" of the June 2020 online article that referred to her saying "hooka looka mooka hooka fooka" on 2GB in May 2020.
The article the sports commentator sued on stated she "refuses to apologise" a few hours before she made an on-air statement that she would never "intentionally offend anybody or hurt anyone's feelings" and was very sorry if she had done that.
Molan also took umbrage with the statement that she "deliberately mocked the names of Pacific Islanders on air".
The 40-year-old denied it was a jibe against Polynesian names, that she was deliberately mispronouncing them for a laugh or speaking in an accent during the broadcast.
Rather, the former 2GB rugby league show co-host said the long-running joke was making light of Ray and Chris Warren mixing up the end of players' names and she was "poking fun of her colleagues", she told the Federal Court.
Justice Robert Bromwich said in reasons published on Tuesday that Molan bears responsibility for being at least thoughtless as to how someone else might interpret what she was saying without the context of that story.
She won on five pleaded imputations, including that it was not proven she had in fact mocked Pacific Islander names, but the judge found both sides had a "measure of success and a measure of failure".
"Dailymail.com needs to substantially improve the care that it takes, or face further and greater awards of damages," Justice Bromwich said in his judgment.
"Freedom of expression must be balanced with responsibility and basic professionalism which was sadly lacking in this case."
Molan gave evidence that she was subsequently subject to a barrage of online abuse and violent threats towards herself and family that left her traumatised.
The news website had argued a defence of truth, with barrister Bruce McClintock SC saying in September 2021 that her attempts of various ethnic groups' accents are forms of "ugly racial stereotypes".
He said Molan showed a lack of contrition and her deficient insight about the effect of her mocking was "tellingly revealed" when she compared it to being "teased in the playground or by her co-hosts".
The trial was played more than a dozen studio tapes that Mr McClintock said showed despicable acts of racism.
In one she says, "I wuv you very long time, very handsome man", but Molan said she was quoting lines from a famous movie rather than trying to imitate the Chinese character.
In another she was heard attempting a Japanese accent and making reference to "you're so good," and "raw fish", which she said is about her favourite food sushi.
Justice Bromwich has allowed Molan to be heard on an injunction to take down the Dailymail.com article if it has not already been removed.
He said it would be advisable for the online publication to promptly follow through with the action after his verdict.
