Deborah Yalcin, 51, died when she was struck at Didcot Parkway station on 3 December last year.
She was a patient at Oxford's John Radcliffe Hospital after being admitted under the Mental Health Act.
A narrative verdict concluded she died as a result of suicide, and a lack of care contributed to her death.
Oxford University Hospitals NHS Trust said it had taken steps, along with Oxford Health NHS Foundation Trust, to improve the systems in place for the care of people who go to A&E with mental health issues "including changes to the way we support and supervise people".
Mrs Yalcin's family became concerned about her health after she claimed she could hear voices, the family's solicitor Irwin Mitchell said.
The natural health therapist, from Downe, south-east London, was awaiting further psychiatric assessment at the John Radcliffe because there were no beds available at the trust's local psychiatric facilities.
After she had been assessed to be in need of admission to hospital under the Mental Health Act, a lack of of one-to-one care contributed to her death and amounted to neglect, the inquest at Oxford Coroner's Court concluded.
Other contributory factors included inadequate detail in handovers and a lack of note-reading by nursing staff, Irwin Mitchell said.
Mrs Yalcin's husband Ahmet described his wife, who did not have a history of mental illness, as "a highly intelligent and caring woman who dedicated her life to helping others and was devoted to our children".
"She was let down by those who were supposed to help her in the most desperate moments of her life," he added.
A mother of three who was killed by a train after absconding from hospital was failed by the NHS trust responsible for her care, a coroner has ruled.