The BBFC noted that the 40 complaints for Black Swan were "proportionately very small indeed" given the amount of people who viewed the Oscar-winning film.
The board's annual report confirmed that the "standout issue" in most complaints was a lesbian oral sex scene.
"While the scene is visually discreet, narratively justified and within the 15 Guidelines criteria, some correspondents felt it was pornographic in nature."
It continued: "That it was a sex scene between two women was an aggravating factor for some who argued that portrayals of homosexual activity should either be restricted to the 18 category, or not shown at all.
"However, the BBFC, in line with broad public opinion, applies the same standards to portrayals of sexual activity, regardless of sexual orientation."
The report also noted that some complainants "had expected to see a film about ballet rather than the story of a young woman's mental disintegration".