Opposition to the bill amending the wording of section 18C of the Act came from Labor, the Greens and several crossbenchers.
The Coalition wanted to replace the offences "insult", "humiliate" and "offend" on racial or ethnic grounds with "harass", and introduce a 'reasonable person test' for claims.
Some critics of the move have expressed concern about the possible impact on social cohesion and inclusiveness.
Labor Senator Lisa Singh says recent polling shows it's not what Australians want.
"From about 1,400 voters, 78 per cent of Australians believe it should be unlawful to offend, insult or humiliate someone on the basis of their race or ethnicity. 76 per cent of respondents who intend to vote for the Coalition, in fact, said they support retaining the words "offend", "insult" and "humiliate". So even if you don't want to listen to the average person on the street, what about listening to some of your own supporters who don't want this law changed?"
The federal Attorney-General George Brandis expressed his disappointment at the outcome.
"We can have a free, robust and healthy liberal democracy that values freedom of thought, speech and expression, and a rich, diverse, magnificent multicultural society at the same time - that one is not a compromise of the other, that one doesn't exist at the expense of the other."
The federal government is separately proposing procedural changes to the operations of the Human Rights Commission.
