The Assistant Minister for Treasury and Finance was one of 23 government senators to vote for the motion moved by Senator Pauline Hanson on Monday afternoon, which acknowledged "the deplorable rise of anti-white racism and attacks on Western civilisation and that it is OK to be white".
Senator Cormann, who is leader of Government business in the Senate, did not give details on the nature of the error, but said he was embarrassed and regretful about the error and took full responsibility.
The Coalition government is blaming an administrative error for its senators backing Pauline Hanson's motion in the upper house that "it's okay to be white".
Attorney-general Christian Porter released a statement which said "an early email advising an approach on the motion went out from my office on this matter without my knowledge".
On Tuesday, in the face of enormous backlash, the government backed away from its support for the motion, with the prime minister saying the original vote was "regrettable".
He claimed the motion "was interpreted in my office as a motion opposing racism", rather than anyone noticing the racist connotations and history of the phrase. "Had it been raised directly with me those issues would have been identified", he said.
Mr Porter said he was reviewing the processes in his office, which had put government senators in a hard position because their advice was to vote for the motion.
"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.
He said there were "50 to 60 motions" every week that were voted on, and that the systems to determine how the government voted had simply broken down.
Speaking to her motion on Monday night, the One Nation leader said anyone who watched the news or social media could see increased attacks on western civilisation and the prevalence of anti-white racism.
Senator Hanson, who declared herself not to be a white supremacist, and fellow conservative crossbenchers didn't attend the recommitted vote.
"Looks like Scott Morrison is suffering from a bad case of it's okay to be white guilt", she tweeted on Tuesday.