The American left the arena after the vault, but later returned to support her team-mates as they claimed silver behind the Russian Olympic Committee.
Biles, 24, scored 13.766 - her lowest Olympic vault score - before withdrawing from the event.
"After the performance I did, I just didn't want to go on," she said.
"I have to focus on my mental health. I just think mental health is more prevalent in sports right now.
"We have to protect our minds and our bodies and not just go out and do what the world wants us to do.
"I don't trust myself as much anymore. Maybe it's getting older. There were a couple of days when everybody tweets you and you feel the weight of the world.
"We're not just athletes. We're people at the end of the day and sometimes you just have to step back.
"I didn't want to go out and do something stupid and get hurt. I feel like a lot of athletes speaking up has really helped.
"It's so big, it's the Olympic Games. At the end of the day we don't want to be carried out of there on a stretcher."
Photo Getty Images Caption: US Olympic gold medallist Simone Biles (left)