"Now we are all part of the story."

CBS News is very publicly grappling with the sexual misconduct allegations against veteran journalist Charlie Rose. The network's journalists are conducting their own investigation in the wake of the Washington Post story that led to Rose's firing on Tuesday.

"I never in a million years thought that we, Charlie Rose, CBS would be involved in this story in this way," Gayle King said Wednesday. "But I also think we're not shy about reporting it. I think that's important."

"It is very important," said Vladimir Duthiers, who joined her on "CBS This Morning."

Duthiers was previously scheduled to fill in for Rose on Wednesday. It's unclear who will co-host alongside King and Norah O'Donnell after the Thanksgiving holiday.

O'Donnell was also scheduled to be off for the holiday on Wednesday, so new correspondent Bianna Golodryga sat in for her. Golodryga has been reporting on the Rose scandal for the network's newscasts.

Related: Here's what Charlie Rose said about sexual harassment before he was fired for it

On Tuesday evening she revealed that three CBS News employees had come forward and alleged "unwanted sexual contact from Rose." The Post story had not included any accounts from inside CBS.

After the report, a CBS News spokeswoman said "this is new information" that was received by management after Rose was fired at lunchtime Tuesday.

King had to decide whether to keep or cancel her scheduled appearance on Stephen Colbert's late night CBS show. She kept it, and told Colbert on Tuesday night that she winced at his jokes about Rose.

Colbert said he was doing his job while King is doing her job, and she agreed.

"It's still very painful. It's still very hurtful," she said, a day after the initial revelations. "Charlie and I — we've worked together, been friends," but she said she has been thinking about "the anguish of those women" who have alleged mistreatment by Rose.

"When I think of the job that we do at CBS and how hard the people work, I want to know we are a top notch broadcast operation and that's why I thought it was important to be here," she told Colbert.

NPR found itself in a similar predicament a few weeks ago when the organization's head of news Michael Oreskes was forced to resign. The organization was lauded for its thorough and transparent reporting on the matter.

This week The New York Times wrote a followup story when Vox described allegations against White House correspondent Glenn Thrush. He has been suspended while the Times investigates.

On Wednesday's "CBS This Morning," King addressed the awkwardness — "now we are all part of the story" — and said it's "important for other women to speak up. We certainly encourage that."

Duthiers added: "I keep thinking about the number of talented women that have left media and entertainment because of an abuser's power over them. The loss of talent that these industries have suffered."

"I think things are changing," King said, "and that is a good thing."