An inquest heard Callum Garland was being cared for at the Lingfield Approach care home in Moortown, which provides 24-hour supervision.
A risk assessment at the home stated Callum, who had a mental age of six, should not climb trees.
Area Coroner Jonathan Leach said care officer Jim Muchesa had given Callum permission to climb a tree on two separate supervised visits to the park opposite Alwoodley Primary School in Moortown on August 6 2015.
On the second visit, Mr Muchesa discovered Callum hanging from a rope in the tree. PC Nicola Pashley told the inquest the rope had been in the tree for “a long time.”
Area coroner Jonathan Leach, said: “We do not know and will never know how the rope came to be around Callum’s neck.”
Recording a narrative verdict, Mr Leach said: “One of his risk assessments specified that he should not climb trees because he had little or no regard for his personal safety.”
Mr Leach said Mr Muchesa had shown “disregard” of the risk assessment.
The inquest head that after discovering Callum hanging, Mr Muchesa called the care home at 6.24pm before calling 999 at 6.37pm and telling the operator a boy was up a tree and refusing to come down.
Forensic pathologist Professor Richard Shepherd had told the inquest there was no evidence of restraint or holding and said that in his opinion Callum’s death was a result of hanging.
After the inquest, Callum’s mother Jacqueline Roberts, of Middleton, Leeds, said: “He rang me that day to say he had a lovely day with his girlfriend and was really happy.
“I strongly feel that social services and the care home have failed him.”
She added: “Callum should not have been allowed to climb that tree and if he had not done so then he would still be here today.
“I will be looking into making an official complaint about how my son was treated.”
Ms Roberts said Callum started displaying problems with his behaviour after suffering a seizure at seven-years-old.
The single mother said she struggling to cope on her own and Callum had to go into care.
Callum was housed at the Lingfield Approach care home from June 2013. Ms Roberts said that despite him being in care they remained close and she would speak on the telephone to him twice a day and would see him every week.
She said: “Callum needed 24-hour care and I could not provide that.
“He was very hyperactive and could be a handful, he did not sleep at night and I couldn’t cope with that on my own.
“You think that a centre that can watch Callum all the time will keep him safe. That’s why he was there – because I was worried I could not keep him safe.
Callum’s father, Russ Garland, a 47-year-old security guard from Wakefield, said he was devastated to lose his son as they had only just got in touch with each other after not speaking for many years.
He said: “He was a great lad and always had a smile on his face.
“It was a shock to us all when he died. There was no way that we will ever think this was suicide, it just wasn’t him.
“We believe he must have got tangled in that rope as he was playing up the tree.”
Steve Walker, director of children’s services at Leeds City Council, said after the inquest: “Callum’s death was a tragedy and our thoughts are with his family and friends at this very difficult time.
“Everyone who knew him whilst he was in our care, is devastated by his loss.
“The safety of children and young people in our care is always of paramount importance to us and something we take very seriously. As a looked after child with additional needs, appropriate measures were put in place to try to keep him safe, which was acknowledged by the coroner, so it is extremely sad that these measures were unable to prevent this tragedy from happening.
“We have undertaken a comprehensive review into the circumstances surrounding this tragic event and as a consequence the care worker who was present at the time is no longer employed by the council.”