Introduced to the Commonwealth country's upper chamber by Pauline Hanson, of the populist, anti-mass migration One Nation party, the motion also asked Senators to acknowledge "the deplorable rise of anti-white racism and attacks on Western civilisation".
"It is a matter of administrative error", Cormann says.
The motion, brought forward by Pauline Hanson on Monday, also declared "anti-white" racism was on the rise in Australia.
On Tuesday, government Senate leader Mathias Cormann - who did not vote in Monday's motion - was forced into the embarrassing claim that the government did not actually support the motion, but that they were confused about what they were voting for. You need guidance from your party leadership on whether to vote for a motion about "anti-white racism" from Australian politics' best known racist?
Attorney General Christian Porter, whose office instructed Government Senators to vote for Senator Hanson's motion, issued a statement saying his office had not picked up the white supremacist connotations of its wording.
"This one was not escalated to me because it was interpreted in my office as a motion opposing racism".
"There is a process involved in determining the position of the government in relation to 50 to 60 motions a week", he said this morning.
Senator Hanson flagged her intention to introduce the motion in September, two months after Canadian right-wing figure Lauren Southern toured Australia and wore shirts with the slogan, 'It's okay to be white'.
"There are administrative processes in place to ensure that as a team we make the right decisions and on this occasion the process failed and I take responsibility for that", Cormann said. Had it been raised directly with me those issues would have been identified'.
Labor and the Greens voted against the motion.
The vote in favour of what many see as a white supremacist slogan sparked a furious backlash and demands for the resignations of ministers who backed the motion.
But the opposition ridiculed the notion that the government did not know what they were endorsing when they supported the motion the first time around.
"Looks like Scott Morrison is suffering from a bad case of it's okay to be white guilt", she tweeted on Tuesday.