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The supermarket chain was targeted by trolls after the first of its three festive adverts featured a Black family.
Now Natasha Mushonga, whose children Malakhai, 11, and Shannel, eight, has spoken about the "hurt" she feels from the racist remarks.
The 34-year-old explained: "It hurts that people think that the colour of your skin determines what type of Christmas you should have.
"There are three adverts to show diversity but you can't win with these people.
"I don't think they wanted it to be about colour diversity. If the advert of another race makes you not want to shop there, well okay then, bye. It's just sad and unnecessary.
"It's racism so you learn to live with it. People should learn to love each other. I feel bad for them that they actually have the time to sit on a computer and post that about an advert."
She added she felt concerned for her children after they appeared in the minute-long advert.
"I'm glad Shannel doesn't know because she can't search for it but Malakhai can because he is in secondary school," Natasha continued.
"He's not bothered in the slightest. I think I prepared them well for what they have to see out there.
"It's obviously ridiculous for people to criticise adverts. It's unfair for the people in it to come to abuse.
"But you can't cure racism - you just have to get on with your life. And you have to celebrate the people are willing to be inclusive, like Sainsbury's.
"People say racism doesn't exist, but if you are on the other side you don't see that."
The advert, titled Gravy Song, sees a young woman phone her father to talk about how she hopes to spend Christmas with her family and enjoy a festive roast. The conversation then quickly turns to her dad boasting about his famous gravy, before singing his gravy song.
Two other adverts from Sainsbury's, focusing on different families, are also set to air over the festive period.
In response to the backlash, a spokesperson issued a statement which read: "At Sainsbury's, we want to be the most inclusive retailer.
"That's why, throughout all our advertising we aim to represent a modern Britain, which has a diverse range of communities.
"We have three stories of three different families in our advertising."
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