Garcia lost 6-1, 6-4 on Tuesday to unseeded Mexican Renata Zarazua, who had reached the second round of a Grand Slam only once before in her career.
Garcia shared snippets of some of the abuse she had received on social media where not only was she targeted but also her family.
The Frenchwoman also took aim at social media platforms for not doing enough to filter abuse while allowing anonymous users to go unchecked.
"Social media platforms don't prevent it, despite AI being in a very advanced position. Tournaments and the sport keeps partnering with betting companies, which keep attracting new people to unhealthy betting," Garcia wrote on Instagram.
"The days of cigarette brands sponsoring sports are long gone. Yet, here we are promoting betting companies, which actively destroy the life of some people. Don't get me wrong, I'm not saying they should be banned.
"But maybe we should not promote them. Also, if someone decided to say these things to me in public, he could have legal issues. So why online we are free to do anything? Shouldn't we reconsider anonymity online?"
Garcia said the messages hurt players, especially after a tough loss when they were already "emotionally destroyed", while also questioning how younger players would react to such abuse.
"I'm just a normal girl working really hard and trying my best, I have tools and have done work to protect myself from this hate. But still, this is not okay," Garcia added.
"It really worries me when I think about younger players coming up, that have to go through this."
Garcia received support from fellow players such as world number one Iga Swiatek and Madison Keys, who both thanked her for speaking up.
American Jessica Pegula said: "The constant death threats and family threats are normal now, win or lose."
