The regulator showed people a number of clips of television as part of a study into audience expectations on potentially offensive content across linear TV and streaming services.
One sketch from Little Britain, originally broadcast in 2002 and available on iPlayer, shows David Walliams as university employee Linda Flint describing an Asian student, Kenneth Lao, over the phone to her manager.
He is described as having "yellowish skin, slight smell of soy sauce ... the ching-chong China man."
The scene is accompanied by a laugh track.
The research participants, who were questioned by polling company Ipsos, viewed the content as "explicitly racist and outdated, and felt that society had moved on", the report said.
It added: "A few participants said they found it funny but seemed embarrassed to say this and could recognise why it would be offensive.
"This content was not considered acceptable for linear TV and many were surprised that it was available on BBC iPlayer.
"Others thought a VoD (video on demand) platform was appropriate because it meant viewers could have the choice about whether to watch the content or not.
"However, they did not think the current rating was enough, wanting a warning about the racist language and an explanation for why it was still accessible. For some, the content was considered too problematic, even for VoD."
The episode currently features a warning before a viewer clicks on the show, reading: "Contains adult humour. Contains discriminatory language."
The report said: "The clip was considered less acceptable because the participants felt it was purposely offensive in stereotyping and targeting an ethnic minority group for comedy purposes.
"Some reasoned that it was important to still show this content to reflect the beliefs of society at the time.
"However, there were concerns that it could normalise racist behaviours which could be repeated by young children."
One respondent, a father from Scotland, said: "If I saw my daughter watching that and then mimicking it, I'd be horrified.
"If kids are watching it, they need it to be explained that that's not acceptable. It's passed off as acceptable behaviour towards fellow human beings that come from a different part of the world."
Episodes of Little Britain, starring Walliams and Matt Lucas, have previously been removed from streaming services following criticism over the use of blackface in the show.
A BBC spokesperson said: "All jokes in our output are judged on context and intent.
"The sketches in which the character Linda Flint makes reference to the appearance or race of a series of people are intended to expose and ridicule some of the outdated prejudices and racism that still exist in parts of British society, which is more apparent when viewing the sketches within the context of a full episode, and across the series as a whole.
"The program is part of the BBC's comedy archive and information is provided for iPlayer viewers about the inclusion of discriminatory language."
Participants in the Ofcom research were also shown a clip from the Jimmy Carr stand-up special His Dark Material, which is streaming on Netflix.
In the special he makes jokes about sexual violence, including: "I don't have to pay for sex, I'm a rapist" and "You can prevent any rape, just say yes."
Once the content starts playing the following briefly appears at the top of the screen: "Maturity rating: 18 / language, sexual violence references, discrimination / Suitable for adults only."
The report said: "Participants believed that joking about rape pushed boundaries too far and felt this could cause harm to victims of sexual abuse.
"Some, particularly female participants, described feeling personally offended by the content."
Other clips shown include those from the Channel 4 show The Handmaid's Tale, Amazon Prime Video's The Boys and Disney animation The Aristocats, which is on Disney+.
The research by Ipsos was conducted with 115 participants between January 12 and February 9 2023.
