The vastly-experienced coach and administrator, after prompting from the chat show host, referred to the American siblings as the "Williams brothers".
His remarks were translated into English and brought a furious reaction from the powerful WTA, which fined him $25,000 and banned him from tennis for a year.
"Serena and Venus [Williams] are without doubts outstanding athletes," said Tarpischev in a statement released by Russia's tennis federation.
"They both perform tennis of top class and embody strength and persistence.
"The situation that has spontaneously emerged during the late night chat show had a bad influence on the perception of tennis in general and splits our friendly and cohesive team."
Tarpischev added that he had harboured no intention to insult the sisters.
"I'm sorry that the joke which was taken out of context and attracted so much attention," he added.
"I think this story does not deserve the attention it is receiving. Everything that I said on TV was said without a malicious intent."
Earlier, WTA chief Stacey Allaster said, "The statements made by Shamil Tarpischev on Russian television with respect to two of the greatest athletes in the history of women's tennis are insulting, demeaning and have absolutely no place in our sport."
Officials of the worldwide women's tennis tour said that the $25,000 fine was the maximum allowed under their rules.
They are also seeking his removal as chairman of Moscow's Kremlin Cup tournament for a year.
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