Andrea Imrie died on 13 January 2024, a week after she fell at Murray Royal Hospital and suffered a brain haemorrhage.
At Perth Sheriff Court on Thursday, the health board admitted it had failed to protect patients on Tummel Ward who were at risk of falls.
It also accepted there weren't enough bedpans for patients who needed them and that staff didn't have an adequate system for checking room movement sensors.
Imrie's bed alarm had been removed the day before she fell and given to another patient. Prosecutor Lisa Duffus told the court the decision wouldn't have been made if there had been enough alarms available.
An infrared sensor in Imrie's room was also not working and it had failed to sound when she got out of bed earlier that morning. Later, staff heard her fall and found her on the floor with blood coming from her head.
She was taken to Ninewells Hospital in Dundee, where a CT scan showed a large haemorrhage. Her condition deteriorated and she died on 13 January.
Peter Gray, representing NHS Tayside, apologised to Imrie's family and accepted that the health board's failings had contributed to her death.
He described the issues as isolated failures in the management of risk, adding they were 'not in any sense deliberate'.
NHS Tayside had issued guidance on managing the risk of falls three months before Imrie's death, the court heard, and has since taken steps to prevent similar incidents.
Sheriff Jennifer Bain KC deferred sentencing after receiving about 500 pages of background material.
