Auriemma said after the Gamecocks' 81-77 victory that Huskies guard/forward Lou Lopez Senechal had bruises on her body from the game.
"It's just appalling what teams do to her now," he said. "It's not basketball anymore. I don't know what it is, but it's not basketball."
Staley fired back Tuesday on her radio call-in show, saying when her team has success, "we're called something other than players that are locked in."
"They play the right way," she continued, "and approach it the right way whether they win or lose. We don't denounce anybody's play. They are always uplifting the game of women's basketball, and when we were getting our heads beat in by UConn for all those years, I said nothing."
South Carolina's victory Sunday was its fourth in the past five meetings between the schools, including the national championship game last April.
Staley's South Carolina teams had been 0-7 against UConn before their recent run of success.
"We've been called so many things and I'm sick of it," Staley said. "I'm sick of it because I coach some of the best human beings the game has ever had."
South Carolina (23-0, 10-0) visits Auburn on Thursday night.