Albert Grannon, 78, today pleaded guilty to manslaughter and possession of a firearm without a certificate following Stanley's tragic death in Sproatley, East Yorkshire on July 26, last year.
He will be sentenced at Sheffield Crown Court on July 2, and has been warned to expect a prison sentence.
Detective Inspector Rebecca Dixon has led the investigation for Humberside Police.
She said: “This was an extremely tragic incident where a six-year-old boy who had all his life ahead of him had it cut so needlessly short.
“Stanley Metcalf was a fun loving, football mad little boy with loving parents and loving siblings. It makes it all the more tragic that it was a member of his own family who was ultimately responsible for his untimely death.
“I am pleased that Albert Grannon has finally admitted his guilt and faced up to the enormity of his actions.
“Up to now he has shown no real remorse for what happened. I hope that now he will realise the effect and suffering that that terrible moment back in July 2018 has had on his parents Jenny and Andy and all those who knew Stanley.
“Despite this, it will never take away the fact that Stanley’s parents, brother and sisters won’t have their beloved son and brother in their lives anymore.
“Stanley has a twin, Elsie. They were inseparable. I can only imagine what she will feel like now and when she reaches any milestones in her life, knowing that she should be sharing them with Stanley.
“There are no winners in this at all. It has been an extremely upsetting case to investigate for all my officers.
“It is a nightmare that Stanley’s family have had to live through every day since last July, and will have to live through from now on.”