"The experience overseas makes the need for penalties crystal clear."
Government minister Linda Reynolds said civil penalties would be examined in a review of the scheme due three years after the laws come into place.
"Business feedback shows market scrutiny as well as reputational risk and reward will drive compliance more effectively than punitive penalties," Senator Reynolds said.
Not enough crossbench senators supported Labor's penalties amendment, which was defeated 29 votes to 26.
Modern slavery practices include people trafficking, forced labour, debt bondage and forced marriage.
More than 40 million people worldwide are believed to be victims of modern slavery, including 4300 Australians.
Labor also wanted forced marriage dropped from the bill's definition of slavery, raising fears it could drive the practice further underground, but the coalition and the Greens teamed up to defeat that amendment.
The draft laws will go to the House of Representatives to approve government changes requiring allowing the minister to send a please explain to companies failing to report.
Under the amendments, the minister also must report annually to parliament about how the regime is working.
Oxfam Australia applauded the government's efforts but chief Helen Szoke said it was disappointing that calls for an independent anti-slavery commissioner were not heeded.
"Oxfam urges for this decision to be revisited as the act is reviewed in the future," Dr Szoke said.
The need for penalties for non-compliance should also be reviewed, she added.