The Women's Tennis Association (WTA) reacted angrily to the remark, imposing a fine of $25,000 along with a ban from the game for a year.
Tarpischev said in a statement: "Serena and Venus are without doubts outstanding athletes.
"They both perform tennis of top class and embody strength and persistence. I'm sorry that the joke which was taken out of context and attracted so much attention.
"I think this story does not deserve the attention it is receiving. Everything that I said on TV was said without a malicious intent."
The $25,000 fine imposed on Tarpischev is the maximum amount allowed under the WTA's rules.