The 34-year-old tennis star lifted a seventh Wimbledon title and record-equalling 22nd major yesterday, before addressing her country's turbulent week.
Five police officers were shot dead by a black extremist in Dallas, Texas, during a march to protest against police brutality.
The peaceful Dallas demonstration was one of several nationwide over the deaths of Alton Sterling in Louisiana and Philando Castile in Minnesota earlier in the week.
"I have nephews that I'm thinking, Do I have to call them and tell them, Don't go outside. If you get in your car, it might be the last time I see you," said Williams in an emotional press conference at the All England Club.
She added: "I don't think that the answer is to continue to shoot our young black people.
"Violence is not the answer. The shootings in Dallas were very sad. No one deserves to lose their life, doesn't matter what colour they are, where they're from. We're all human."
Gun violence has personally touched Williams and her family in the past.
In September 2003, her elder half-sister Yetunde Price was gunned down in a drive-by shooting in Compton, the crime-plagued suburb of Los Angeles where Serena grew up.
Price was sitting in a car with her boyfriend at the time of the shooting.
He escaped uninjured in the incident in which a neighbour said a dozen shots were fired.
"We have to learn that we have to love one another," added Serena.
"It's going to take a lot of education and a lot of work, I think, to get to that point.
"But I think, in general, the entire situation is extremely sad, especially for someone like me. It's something that is very painful to see happening."
On Friday, NBA star Carmelo Anthony urged athletes to "step up" and "demand change".
Anthony, a New York Knicks forward who could win an unprecedented third men's Olympic basketball gold medal in Rio, posted a message on social media calling for athletes to help change a system that he described as "Broken. Point blank period.
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