Tarpischev referred to Serena and her sister Venus Williams as "the Williams brothers" while on a US chat show and later apologised for his comments, which he said were "made without malicious intent".
"I thought they were very insensitive and extremely sexist as well as racist at the same time," Serena told BBC Sport.
"I thought they were, in a way, bullying. I just wasn't very happy with his comments. I think a lot of people weren't happy as well."
Serena has won 18 Grand Slam singles titles throughout her career and is the reigning US Open champion.