Disability campaigner John Davidson, who has Tourette's, could be heard shouting as Sinners stars Michael B Jordan and Delroy Lindo presented an award during the British film and TV awards ceremony on February 22, which was broadcast on the BBC with a two-hour time delay.
The BAFTA board said an independent review of the incident found issues with "planning, escalation procedures and crisis co-ordination arrangements" for the awards, but it "did not find evidence of malicious intent on the part of those involved in delivering the event".
A statement from the BAFTA Board said: "We apologise unreservedly to the Black community, for whom the racist language used carries real pain, brutality, and trauma, to the disability community, including people with Tourette Syndrome, for whom this incident has led to unfair judgment, stigma, and distress; and to all our members, guests at the ceremony and those watching at home.
"What was supposed to be a moment of celebration was diminished and overshadowed. We have written to those directly impacted on the night to apologise.
"The review is clear that while this was not a failure of intent, BAFTA's planning and processes have not kept pace with its diversity and inclusion goals.
"We did not adequately anticipate or fully prepare for the impact of such an incident in a live event environment and as a result our duty of care to everyone at the ceremony and watching at home fell short."
The academy said work was under way as a priority to address the areas of improvement specified in the review, carried out by Rise Associates, to "reduce the risk of this happening again".
It comes after an investigation found the BBC breached its editorial standards when it broadcast the slur.
An investigation by the BBC's executive complaints unit found the inclusion of the slur was "highly offensive" and "had no editorial justification", but it added broadcasting it was unintentional.
The report confirmed the BBC's chief content officer has sent letters of apology to Lindo, Jordan and Davidson.
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