She is being sued for wrongful death by Barson's family.
'I am devasted and heartbroken by this accident. "I'm speechless, and I'm just ..."
That's when the moderator jumped in to briefly stop the press conference.
Reporters at the London tournament asked Williams on Monday about her "emotions" this past month and how she was coping, and for the first few minutes she handled it well, keeping her answers focused on her game.
Earlier last month, Venus Williams was involved in a deadly vehicle accident in Palm Beach Gardens, Florida.
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According to the police report, Ms Barson told police she had approached an intersection, slowing for a traffic light.
A spokesman for Palm Beach Gardens police in Florida confirmed to the BBC they were investigating a fatal crash involving the Grand Slam champion. She said she was grateful to return to Wimbledon.
When questioned about how she was dealing with the crash, Williams teared up.
"I am devastated and heartbroken by this accident", Williams wrote in the post.
The police report estimated Williams was travelling at about 8kmh at the time of impact and was not distracted or suspected of any drug or alcohol use.
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Per an official police report obtained by TMZ Sports , the accident occurred June 9 in Palm Beach Gardens. The victim, Jerome Barson , was transported to the hospital, suffering from head trauma.
After her 7-6 (9/7), 6-4 victory over Elise Mertens in the Wimbledon first round, world number 11 Williams was repeatedly asked about the incident by the media and eventually became so emotional she began to cry.
Esther Linda Barson was driving this Hyundai Accent when they T-boned the auto driven by Venus Williams.
According to The New York Times, Jerome Barson was the 78-year-old passenger, who died two weeks after the accident.
While Williams was not given a citation by police for the crash, she was found at fault for failing to yield the right of way.
Esther Barson, 68, was traveling west on Northlake Boulevard and told police she proceeded through a green light.
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This is Williams' 20th Wimbledon, according to ESPN.