On the BBC's Daily Politics show, Mackenzie was accused by Labour MP Chris Bryant of lying in a heated debate over the paper's coverage of the 1989 Hillsborough tragedy, in which 96 Liverpool fans lost their lives.
Presenter Andrew Neil, who had to calm the pair down at one point, asked Mackenzie if he felt regret or remorse over a notorious article published on April 19, 1989, and headlined 'The Truth'.
To this, the former editor replied: "Probably, yes I do."
The Sun's article alleged that the disaster followed "mass drunkenness" among Liverpool supporters, and that some fans had urinated on police and picked victims' pockets as their bodies lay on the pitch.
The News International paper claimed that the allegations came from unnamed South Yorkshire police officers.
After the report was published, The Sun was subject to a boycott on Merseyside, which still lasts in part to this day, despite various attempts by the paper to apologise.
Asked if he had any regrets over the story, Mackenzie said: "If I could revisit Hillsborough, certainly, I would do it in a different way. I would do it in the way the other newspapers did it.
"They basically ran the story and said 'big fury over...' and I wish I had done that, yes."
In October, more than 16,000 people signed an e-petition calling on The Sun to reveal its sources behind the notorious Hillsborough story.
During his appearance at the Commons culture media and sport select committee investigation into newspaper phone hacking in November, News International chairman James Murdoch was also pushed on the ongoing controversy surrounding the story.
Steve Rotherham, a committee member who is the MP for Liverpool Walton, asked Murdoch whether the fact that The Sun had "got away with it" in 1989 could have led to a belief within News International that it "could get away with things" again.
Murdoch strongly denied the suggestion, but again apologised unreservedly for the coverage. He also refused to rule out closing the paper if it was also found culpable of criminal behaviour.