Carneiro left Chelsea in September 2015 after being publicly criticised by then manager Jose Mourinho
"Even though I don't have a presence on social media -- I think I have made one post ever in my life -- some of the threats of sexual violence and death threats make it through," she told the Daily Telegraph.
"They (the abusers) just seem to be faceless cowards and they should be answerable to legislation."
Carneiro, 43, left Chelsea in September 2015 after being publicly criticised by then manager Jose Mourinho for going onto the pitch to treat a player during a home game against Swansea City.
Earlier this year she settled a constructive dismissal case with Chelsea, who apologised "unreservedly" over her treatment, and she also reached a discrimination settlement with Mourinho.
Carneiro, who now works at her own clinic in London, feels not enough is being done to eradicate sexism in football.
"I think sexism is the least challenged form of discrimination." she said.
"Anti-Semitic and other racist comments are widely condemned and I don't think that is the case (with sexism) and it begs the question what that leaves room for behind the scenes.
"It is widely accepted that football has a discrimination problem. I really do feel that way, but I think it is the least challenged form of discrimination."
Carneiro said she had been "stunned" by the reactions of male colleagues in the medical profession when she made it clear she wanted to train as a football medic.
"Seeking specialist training in certain sports, male colleagues found that quite surprising," she said.
"There was very much a dialogue of bringing attention to my gender or objectifying me in some way.
"They described that as a limit to my career progression in that direction, which I was stunned by. It was a dialogue more appropriate for the 1950s."