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"His insensitive comments are an embarrassment to the nation, particularly for someone who holds a national position," the YCL said in a statement to the South African Press Association (SAPA).
The YCL urged him to withdraw his statement and apologise to the bereaved family, who are mourning the loss of their loved one.
De Villiers made the comment before Roux was granted 100,000 rands (13,700 U.S. dollars) bail in the Pretoria Magistrate's Court on Aug. 30.
The coach said the team supported Roux not on the deed, but on the circumstances that led to the situation developing.
However, the YCL said that nothing could justify murdering someone. It called Roux an "ill-disciplined" and "intoxicated" rugby player.
Pretoia metro policemen Ntshumane Johannes Mogale was killed in Pretoria on Aug. 27, allegedly by Roux.
At Mogale's memorial service on Thursday, metro police regional director Moloko Racheku said that he had shuddered after hearing de Villiers comment.
The director said that the Springboks obviously knew something about the incident that the rest of the public did not.
The Times newspaper in Johannesburg reported that De Villiers could face a disciplinary hearing with the South African Rugby Union for his comment, and other comments made in the past.
The Springboks face Australia in Bloemfontein on Saturday. Springbok captain John Smit declined to comment on the matter.
"Please guys, let's stick to the rugby," he said when asked at a Friday news conference.