The Tourette syndrome campaigner who shouted the slur said he was "deeply mortified" and what he said was "not a reflection of my personal beliefs".
The highly offensive word could be heard as Sinners stars Michael B Jordan and Delroy Lindo, who are both black, were presenting the award for best visual effects during Sunday's ceremony.
Host Alan Cumming had earlier told the audience that Tourette syndrome advocate John Davidson was in attendance.
The incident prompted the British Academy of Film and Television Arts to apologise for "offensive language that carries incomparable trauma and pain for so many".
"We would like to thank Michael and Delroy for their incredible dignity and professionalism," it said.
Davidson, a Scottish campaigner for people with Tourette syndrome, who inspired the BAFTA-nominated film I Swear, said in a statement Monday he was "deeply mortified if anyone considers my involuntary tics to be intentional or to carry any meaning".
Tourettes Action - a Tourette syndrome charity - called for understanding of the condition.
"We deeply understand that these words can cause hurt but at the same time, it is vital that the public understands a fundamental truth about Tourette syndrome: tics are involuntary. They are not a reflection of a person's beliefs, intentions, or character," said Emma McNally, CEO of Tourettes Action.
Tourette syndrome, a neurodevelopmental disorder, is characterised by sudden, involuntary movements or sounds called tics that tend to wax and wane but can worsen with excitement or anxiety.
They may appear to be purposeful but are not, and the NIH's National Institute of Neurological Disorders and Stroke's Tourette information page says people trying to suppress them often report a buildup of tension before a tic erupts.
The Tourette Association of America says about 10-15 per cent of people with the syndrome experience a kind of vocal tic called coprolalia - involuntary swearing, slurs or other socially unacceptable words or phrases.
After the slur was shouted during Jordan and Lindo's presentation, Cumming apologised to the audience at London's Royal Festival Hall for the "strong and offensive language".
"Tourette syndrome is a disability and the tics you have heard tonight are involuntary, which means the person who has Tourette syndrome has no control over their language," Cumming said.
"We apologise if you were offended."
The epithet could be heard when the BBC broadcast the ceremony about two hours after the live event. The broadcaster apologised for not editing it out before the broadcast.
"Some viewers may have heard strong and offensive language during the Bafta Film Awards," the BBC said in a statement.
"This arose from involuntary verbal tics associated with Tourette syndrome, and as explained during the ceremony it was not intentional.
I Swear won two BAFTAs, including best actor for Robert Aramayo, who plays Davidson.
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