Anderson issued the apology Friday after making the comments during a conversation with the team during fall camp.
"In the course of that conversation, I used a phrase regarding victims of wrongdoing to magnify that message to our team, but after reading my comments in the transcript that was released, I realize my choice of words was hurtful," Anderson said in a statement. "I regret the words I used, and I apologize to anyone who has bravely come forward with allegations of wrongdoing."
A recording of Anderson's discussion with the team surfaced shortly before Utah State was set to face Oregon State in the inaugural Jimmy Kimmel LA Bowl on Saturday. Utah State University has said it was investigating the comments.
The recording was obtained by The Salt Lake Tribune and mentioned in a lawsuit filed this week by a female student who says the school mishandled her sexual-assault report involving a football player.
"We have to do everything we can to encourage and protect anybody who has been the victim of a wrong, or whose personal rights have been violated. Anyone who knows me knows how strongly I feel about this," Anderson's statement continued. "Giving victims a safe platform to address wrongs they've suffered is always the right thing to do, and something I'll always stand for."
The Salt Lake Tribune also obtained a recording of Utah State University police chief Earl Morris, who stepped down on Thursday. Morris was heard warning players in a separate meeting about having sex with women who are members of the Church of Jesus Christ of Latter-day Saints because he said they might later feel regret and report it as nonconsensual.