"My immediate reaction was did she know who it was? No. What colour were they? She said it was a black person," he said.
"I went up and down areas with a cosh, hoping I'd be approached by somebody - I'm ashamed to say that - and I did it for maybe a week, hoping some black b------d would come out of a pub and have a go at me about something, you know? So that I could kill him."
Neeson made the comments during an interview to promote Cold Pursuit, his latest film, in which his character seeks revenge for his son's murder.
He later denied being racist but said he had simply been honest and that people should stop pretending to be politically correct.
The actor enrolled at Queen's in 1971, reading physics and computer science but left to work for Guinness before graduating.
In 2009, he received an honorary doctorate from the university for his Outstanding Contribution and Service to the Arts.
Queen's University did not immediately respond to a request for comment.
This article originally appeared on the Daily Telegraph.