Thomas Gallagher, 16, was discovered by a member of the public in Old Kays Park in Tottington, Bury, in July 2015.
An inquest concluded the schoolboy took his own life and police shortcomings did not contribute to his death.
But an Independent Police Complaints Commission (IPCC) report found Greater Manchester Police's (GMP) conduct was "below the standard expected."
The teenager's parents criticised police, saying there had been serious failings in the handling of the case, the Manchester Evening News reports.
In a statement they said: "We explained his vulnerabilities concerning his recent mental health history. Subsequently two members of the public found Tom five hours later. GMP failed to respond at all."
The IPCC found police delayed looking for the schoolboy because of staffing shortages in the Bury division, which were "foreseeable".
"No officers were deployed...until the discovery of Thomas' body some five hours later," the investigator found.
The report said the response of four officers and a radio operator was "unsatisfactory".
It said the conduct of an inspector, a police sergeant, an acting police sergeant, a police constable and a civilian radio operator, "whilst not amounting to misconduct, did fall below the standard expected."
IPCC Associate Commissioner, Guido Liguori, recommended GMP "should address" the "under-resourcing" of the police division in Bury as well as "ensuring police officers and staff are properly supported" for "the benefit of the local community."
Ch Supt Chris Sykes from GMP's Bury division said: "Thomas Gallagher's death was a tragedy and our deepest condolences remain with his family.
"Unfortunately, it was not possible for GMP to resource the original missing report, due to staff abstractions and a higher than usual number of incidents on the night."
Changes have already been implemented in Bury, including new shift patterns, to ensure the force could respond to unanticipated spikes in demand in future, he added.
He said: "Whilst the jury concluded that none of the shortcomings in GMP's response caused or contributed in any way to Tom's death, we fully acknowledge the comments made by the jury in delivering their conclusion at today's inquest. We will also await the coroner's report on any recommendations."

Saints won 13 trophies under Harrison, who has left after five and a half years in charge to join Hartlepool.
Ruscoe, 39, is in interim charge along with Steve Evans following Harrison's departure.
"He's won so many [trophies] and he's done such a good job, how do you go and follow that now?" Ruscoe said.
"Me and Steve want to give it our best and the lads will as well. They've been great in the last few days as we've taken over."
Saints begin their preparations for the Champions League qualifiers with a friendly against an Anglesey Island Games XI on Tuesday, 6 June.
Club owner Mike Harris hopes Ruscoe and Evans will be permanent replacements, but says one of them must complete their coaching qualifications.
Former club captain Ruscoe, who joined Saints as a player in 2001 and holds a Uefa A coaching licence, wants the job on a permanent basis.
"I've been in football full-time for over 20 years so it's something I want to do for the rest of my career," Ruscoe told BBC Radio Shropshire.
No officers were deployed to search for a vulnerable teenager who was later found dead, the police watchdog said.
[NEXT_CONCEPT]
Interim manager Scott Ruscoe says Craig Harrison will be a hard act to follow at Welsh Premier League champions New Saints.