Iwan Lewis, 36, of Penygroes, Gwynedd, was a patient at Ysbyty Gwynedd, Bangor, before his death last May.
Speaking at his inquest, his mother Elizabeth Lewis accused Betsi Cadwaladr health board of not listening to her concerns.
The trust said it would give the family a written apology.
Coroner Nicola Jones recorded a narrative verdict, saying it was impossible to say for certain whether Mr Lewis' death was an accident or suicide.
The inquest in Caernarfon previously heard that Mr Lewis, a paranoid schizophrenic, had been sectioned at the hospital's Hergest unit for an alleged assault on his mother, who cared for him.
He was later moved to the Cynan ward, where the day before his death he was refused extra medication for feeling agitated.
A police officer also visited the ward a few days earlier to speak to Mr Lewis about his bail arrangements, a visit which consultant psychiatrist Dr Olufemi Adebajo told the inquest he was "extremely unhappy" about.
After the hearing, North Wales Police said the officer had acted "perfectly reasonably".
Supt Nigel Harrison confirmed Mr Lewis had previous contact with the police and an officer did visit him in hospital to undertake a "legal requirement" and "having sought permission to do so".
He said: "As part of our multi agency work with our partner agencies, we regularly hold meetings with the local health board, where the now raised concerns by the consultant will be discussed.
"The coroner made it clear that the officer acted perfectly reasonably and we are satisfied that our officers acted entirely appropriately throughout."
Speaking at the inquest on Friday, the trust's clinical director of mental health, Dr Sandeep Matthews, said they "could have engaged more with Mrs Lewis, and taken her views on board".
Questioned by the coroner, he agreed that "on the balance of probability" the trust had breached their duty of care to Mr Lewis.
As well as an apology to the family, the trust said it was making several improvements which included better co-operation with the police, better communication with the families of patients and improvements in documentation.

Feeney, 29, previously spent time on loan at Blackburn at the end of the 2013-14 season, making six appearances.
The former Bournemouth and Millwall man, who finished last season on loan at Ipswich Town, made 71 league starts for Bolton during a two-year contract.
Rovers finished 15th in the table last term, 15 points clear of relegation.
Feeney is the club's fourth signing so far this summer, joining full-back Stephen Hendrie plus strikers Anthony Stokes and Danny Graham.
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A senior health board official has admitted a breach in the duty of care to a mentally ill patient whose body was found in the Menai Strait.
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Championship club Blackburn Rovers have signed former Bolton Wanderers winger Liam Feeney on a two-year deal, with the option of a further year.