The jury at Wakefield Coroner’s Court returned a narrative verdict setting out the circumstances surrounding Matthew Lee Johnson’s death.
Mr Johnson, 28, was found hanging in his cell in the prison’s First Night Centre on June 24, 2016, and died two days later at Leeds General Infirmary.
Although prison staff resuscitated him and paramedics stabilised him, the father-of-five suffered severe and irreversible hypoxic brain injury.
The inquest heard Mr Johnson, who had never been in prison before and strenuously denied the charges he faced, had a history of mental illness, self-harm and suicide attempts.
Staff at the police station and courts had noted concerns about Mr Johnson harming himself, so prison reception staff opened an Assessment, Care in Custody and Teamwork (ACCT) document as part of monitoring procedures.
However, two mandatory ACCT provisions were not carried out as they should have been and hourly observations were missed in the two hours before Mr Johnson was founding hanging.
An officer accepted in evidence that they had failed to comply with ACCT requirements, and that staffing shortages meant none of the prisoners in the First Night Centre could have received the support they needed.
His brother, Kyle, said: “Matthew was a family man - a father of five who was completely devoted to his children, who were always his number one priority.
"We strongly believe that Matthew would still be here today if HMP Leeds provided the care he needed."
The family was represented during the hearing by INQUEST Lawyers Group member Charles Myers, of Minton Morrill, and Richard Copnall, of Parklane Plowden Chambers.
Mr Myers said: “This is yet another tragic case at HMP Leeds of a vulnerable young man whose risk to himself was appropriately identified, yet not managed correctly.
"This is unfortunately the latest in a succession of inquests in which we have been instructed where the mandatory ‘benchmarked’ staffing levels put in place at ministerial level have had a direct impact on the ability of the staff to look after vulnerable prisoners.
"I can only hope that eventually the Ministry of Justice will realise that they simply have to act if we are to avoid such unnecessary losses of life in future."
He added that it was encouraging to hear the prison had finally put in place a more robust quality control process for ACCT documents.
A Prison Service spokesman said: “This is a tragic case and our thoughts are with Matthew Johnson’s family and friends. We take the welfare of prisoners extremely seriously and HMP Leeds is introducing a number of steps to improve the standard of care, including extra training for staff.
Other measures include dedicated points of contact for any prisoner at risk, the recruitment of 2,500 extra frontline officers nationally, and a suicide and self-harm project to reduce such deaths.
The spokesman added: "We will now consider carefully the findings of the inquest to identify lessons learnt.”
Official data shows 121 prisoners took their lives while in prison custody in England and Wales last year.