Rutgers University Athletic Director Tim Pernetti only suspended and fined coach Mike Rice after viewing a video of him berating and hitting players.
Mr Rice eventually lost his job this week as clips of his furious rants were aired on national TV networks.
But as Mr Rice was not fired earlier, he is due a $100,000 (Â£65,000) bonus.
His contract entitled him to the cash reward for finishing the 2012-13 season.
Critics of the New Jersey university say Mr Rice should have been fired when administrators first saw the video last year.
In his resignation letter, Mr Pernetti said he hoped his tenure at Rutgers would "not be judged by this one incident".
The 42-year-old added that when he first saw the video, his "first instincts... was to fire him immediately".
However, he said the consensus at the time was "university policy would not justify dismissal".
In an earlier statement, Mr Pernetti said that it had been his decision to "rehabilitate" Mr Rice, "but I was wrong".
The footage, shown for the first time publicly on sport broadcaster ESPN on Tuesday, was shot during team practices between 2010-12.
Mr Rice is seen shouting homophobic slurs, hurling balls at players, kicking, pushing and grabbing them.
At a campus news conference on Friday, university president Robert Barchi said: "I want to apologise to the entire Rutgers community for the negative impact that this situation has had on Rutgers.
"I also apologise to the LGBTQ community and all of us who share their values for the homophobic slurs shown on that video. I personally know how hurtful that language can be."
Mr Rice was recruited in 2010 to be head basketball coach at Rutgers, which finished last season near the bottom of their league, the prestigious Big East Conference.
A US university's sports chief has resigned amid widespread criticism of his failure to sack a volatile and abusive basketball coach.