The government leader in the Senate, Mathias Cormann, the foreign affairs minister, Marise Payne, and five other Coalition senators were paired with senators who meant to vote against the motion but were not in the Senate, meaning those Coalition senators also supported the motion but did not vote.
"We should have opposed the motion when it came up in the Senate yesterday", he said.
Mathias Cormann, leader of the government in the Senate, also took responsibility for what he said was a mistake.
Finance Minister Mathias Cormann has apologised after Government senators voted for a Pauline Hanson motion that used far-right slogan "It's OK to be white", saying the vote was the result of an "administrative error" and the Government had previously chose to vote against the motion.
Senator Cormann said the government made a decision to oppose the motion and instead issue a statement that it deplored racism in all forms.
The One Nation Leader says "anti-white racism" is on the rise and insists it must be called out.
It is true that the slogan "It's Okay to Be White" is thought to have originated among alt-right users of the 4chan anonymous message board, but it appears to be Senator Keneally and the other opponents of Ms Hanson's motion who have played into their hands - as the slogan's reputed goal is to goad leftists into voicing opposition to the statement, revealing what its proponents consider to be a latent anti-white bias.
Labor also voted against the motion and attacked Coalition senators for backing it.
Coalition senators supported Senator Hanson's motion, as well as crossbench senators Peter Georgiou, Cory Bernardi, David Leyonhjelm and Fraser Anning.
Independent senator Derryn Hinch labelled it "obscene".
He said Ms Hanson was "in a race" with another of her colleagues "to the bottom of the sewer" by seeing "who can be the biggest, the loudest, racist bigot".
But other senators denounced her motion.
The Liberals just sided with One Nation and Frasier Anning on a motion straight out of the alt-right playbook.
"This is a phrase used by white supremacists", Labor senator Penny Wong told reporters.