Sharapova was responding to comments from Williams in a Rolling Stone interview in which she criticised an "anonymous" player widely believed to be the Russian, and appeared to refer to her boyfriend Grigor Dimitrov as "the guy with a black heart".
Sharapova said of the remarks: "As for myself, or whether it was about somebody else, nothing personal, you know.
"At the end of the day, we have a tremendous amount of respect for what we do on the court. I just think she should be talking about her accomplishments, her achievements, rather than everything else that's just getting attention and controversy.
"If she wants to talk about something personal, maybe she should talk about her relationship and her boyfriend that was married and is getting a divorce and has kids.
"Talk about other things, but not draw attention to other things. She has so much in her life, many positives, and I think that's what it should be about."
Sharapova also added to criticism of Williams over controversial comments on a high-profile teenage rape case in Ohio.
"Obviously I have a tremendous amount of respect for Serena and what she's achieved on the court. You can never take anything away from that," 2004 Wimbledon champion Sharapova told reporters.
"I was definitely sad to hear what she had to say about the whole case."
Williams has since apologised after quotes attributed to her suggested the victim had been drunk.
Williams beat Sharapova 6-4 6-4 in the French Open final earlier this month, and is favourite to win her sixth Wimbledon title.
The defending champion is set to hold her pre-tournament press conference on Sunday.
Serena has since launched a charm offensive as she sought to broker a truce with Sharapova and calm the storm surrounding comments she made about a rape victim.
"I made it a point to reach out to Maria because she was inadvertently brought into the situation by assumptions made by the reporter," a smiling Williams told reporters.