Rutgers President Robert Barchi said he accepted Pernetti's resignation and apologized to numerous groups who may have been offended by the words and actions depicted in a video of Rice.
"I recognize and understand the gravity of recent developments with the men's basketball program," Barchi said at a news conference. "I want to personally apologize to the entire Rutgers community for the negative impact this situation has had."
Rice was fired Wednesday, one day after ESPN's "Outside the Lines" program showed the video of the coach verbally and physically abusing players during practice last November. Rice is seen yelling obscenities and homophobic slurs at players, throwing basketballs at them and pushing and shoving them.
Pernetti, on the advice of school lawyers, suspended Rice for three games and fined him $50,000 in December. That decision came under question when the video became public this week.
He stated in his resignation letter his first instinct after seeing the video was to fire Rice immediately but Rutgers decided to "follow a process involving university lawyers, human resources professionals and outside counsel."
"In connection with the incident ... as was the case with all other matters which I handled on behalf of the university, I always tried my best to do what is right," Pernetti's letter stated. "I have spent a great deal of time reflecting on the event, which led to today."
Pernetti, 42, had been director of athletics at Rutgers, his alma mater, since April 1, 2009. He was credited with moving the Rutgers athletic program from the Big East Conference to the Big Ten Conference, effective in the 2014-15 academic year.
Some instructors at Rutgers have called for the resignation of Barchi, who said he was aware of the video in November but hadn't viewed it until the ESPN airing.
Barchi said he would soon hire an interim athletic director before finding a person to take the position on a permanent basis, and then the school would being recruiting a new basketball coach.