Jennifer Slack, 63, and her husband Graham, 62, were found with their wrists tied together on mud banks at Breydon Water, Norfolk last September.
An inquest in Norwich heard Mrs Slack had been suffering from depression following the death of her father.
Mrs Slack's GP practice was urged by the coroner to ensure urgent letter referrals were sent the same day.
The inquest was told Mrs Slack had been treated for depression and anxiety since the mid-1990s but became worse after her father died in spring.
After telling a nurse at Park Surgery in Great Yarmouth that she had questioned the point of life, Mrs Slack's GP wrote a letter on 27 September requesting an urgent psychiatric referral.
However the inquest was told the letter was not sent until the following day and was not received by mental health services until after her death.
Mr and Mrs Slack's bodies were recovered from Breydon Water on 29 September.
A note found by police in the couple's abandoned car said the pair were taking their own lives adding "My wife has anxiety and we feel there is no help".
The Norfolk coroner, Jacqueline Lake, who recorded a verdict of suicide, said she was satisfied the GP practice had since made the necessary improvements with regard to processing urgent referrals.
A coroner has criticised a lack of urgency in securing psychiatric help for a woman who took her own life.