Oyelowo played Dr Martin Luther King Jr in the film, which told the true story of his fight for equal voting rights.
Speaking to Screen Daily as part of its Screen Talks series, he described how the cast's decision to shine a light on racial issues was viewed as "stirring shit".
"Six years ago, Selma coincided with Eric Garner being murdered. That was the last time we were in a place of 'I Can’t Breathe' [a slogan for the movement taken from Garner’s last words before he died at the hands of US police]," he said.
"I remember at the premiere of Selma us wearing 'I Can’t Breathe' T-shirts in protest. Members of the Academy called in to the studio and our producers saying, 'How dare they do that? Why are they stirring S-H-I-T?' and 'We are not going to vote for that film because we do not think it is their place to be doing that.'"
'I Can't Breathe' has become a slogan used by the Black Lives Matter movement.
He went on to say that this criticism from some Academy members meant that Selma did not get the awards season recognition it deserved at the Oscars, thus "birthing" the #OscarsSoWhite movement.
"It’s part of why that film didn’t get everything that people think it should’ve got and it birthed #OscarsSoWhite," he said. "They used their privilege to deny a film on the basis of what they valued in the world."
Ava DuVernay – director of Selma and When They See Us – lent her support to Oyelowo's comments by sharing the story on Twitter with her own take. She wrote: "True story."
The Academy has also tweeted in response: "Ava & David, we hear you. Unacceptable. We’re committed to progress."
For more information on how you can support Black Lives Matter, please visit its official website or donate here. Readers can also donate to the UK anti-discrimination group Stand Up To Racism, and the Unite Families & Friends Campaign, which supports those affected by deaths in police, prison and psychiatric custody.
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