Kearney, who had been placed on paid leave in November, told the Austin American-Statesman Saturday she engaged in a "consensual intimate relationship" with an "adult student-athlete" from July to December in 2002.
The male student reported the relationship to UT officials in October.
Kearney said she is unsure why the decade-old relationship is resurfacing now.
"I don't have control of those things," she said. "Those are things that haunt you, so I have chosen not to focus [on that] because I don't know. At the end of the day, I've had to ask myself, 'Does it really matter?' "
Derek A. Howard, Kearney's attorney, issued a statement saying: "We believe that Ms. Kearney has been subjected to a double standard and has received far harsher punishment than that being given to her male counterparts who have engaged in similar conduct."
Kearney and Howard declined to say if they plan to take any legal action.
"I don't think that's important to be discussing at this point in time," Kearney said. "It's not something I want to delve into right now."
A university statement said assistant coach Rose Brimmer will serve as the interim head coach until a replacement for Kearney is found.