The shadow home secretary’s shocking admission came as she described the extent of the sexist and racist abuse she had received over recent years.
The MP for Hackney North and Stoke Newington said the threats had now become so bad she was frightened to walk the streets alone.
Diane Abbot said she had racist abuse hurled at her after the Article 50 vote
They're not entitled to say that I am black filth and I should be hanged
She said: “When Jo Cox died, obviously my first thought was for her children and her husband, and then her friends and family, and the people of Batley and Spen, and we'd lost a tremendous MP.
"But I also thought, maybe you can't shrug off these death threats anymore… maybe something can happen.
"Since then, I try not to walk on my own anymore. I don't drive. I used to walk around Hackney on my own, I don't do that anymore, and I am getting new security alarms on my house.”
During an interview, the shadow home secretary revealed the shocking abuse she had received
Ms Abbott said she believed the abuse towards her was worse because she was a black, female MP.
“If you're a woman you get a kind of abuse, the rape threats, telling you you're ugly, you get a kind of abuse that male MPs just do not get. They just do not get,” she continued.
“I'm finding it increasingly difficult because it gets in your head, it gets in your head, and as I say, in the current climate you start to think 'well, maybe, these threats, maybe they're real?’.”
Brexit: Which parts of the UK had the majority vote? Fri, February 17, 2017
Much of the North East of the United Kingdom voted to leave the European Union including Sunderland, Gateshead, Darlington, Durham, Hartlepool, Middlesbrough, Stockton, Redcar and Cleveland, North Tyneside and South Tyneside, and Northumberland. Newcastle was the only borough to vote to remain.
Play slideshow Getty Images 1 of 8
GREAT YARMOUTH: The town of Great Yarmouth on the East Coast of England voted by 72% to leave the European Union.
The Labour MP came under fire earlier this month after she failed to turn up for the vote on the second reading of the Article 50 bill.
She claimed she had a migraine and was too ill to make it to Parliament, despite being pictured in the pub the night before.
Asked about the reaction she had received from people after missing the crucial vote, Ms Abbott opened up about the extent of the online abuse.
She said: “People are entitled to be angry, but they're not entitled to say that I am black filth and I should be hanged. Do you see what I mean?
"There's a difference between saying 'I don't like what Diane Abbott did' or 'I don't agree with her on some things, and just this really angry racist abuse."