Underwood and Osbourne fell out during an episode on March 10, during a tense on-air discussion about racism that led to Sharon's departure from the show.
Sheryl addressed viewers at the top of Monday's episode and revealed she feared being perceived as "the angry black woman".
She also addressed Osbourne's demand that she should not "dare cry" to win sympathy during their awkward clash.
"I'm not tearing up because I hurt your feelings or want some sympathy," she said. "I'm crying because I have to restrain myself... To be told you can't do something... I'm a grown-a** woman, but you have to suppress that."
The entire episode of "The Talk" was devoted to racism and the March 10 showdown, which was sparked by Osbourne's defence of her friend Piers Morgan following his outburst about Meghan Markle, the Duchess of Sussex on a British breakfast show. Morgan had been accused of racism for comments he made about the royal and Sharon stated, "I feel like I'm about to be put in the electric chair because I have a friend who many people think is racist, so that makes me a racist."
The tense encounter came to a head when Osbourne turned to her co-host and asked her to be precise about how Morgan had been racist and as Sheryl started to respond, Sharon raged, "Don't you dare cry."
On Monday's show, Sheryl also confirmed she had not been in contact with Osbourne since the episode, although Sharon had texted her. Underwood said she did not respond because their on-air stand-off was under an internal investigation.
Underwood was defended by another co-host, Elaine Welteroth, who said she believed Osbourne "was not listening and went off the rails into disrespect", while shooting down reports that she and Sheryl had conspired to "attack" Osbourne, adding, "That is absolutely, categorically false."
"What you saw were two women who were maintaining their composure, their dignity and their respect every step of the way and were not being heard," Welteroth added.