Martin Bell, 20, Frank Hudson, 19 and two 17-year-olds who cannot be named posed for the disturbing footage which they posted on Instagram.
They admitted causing unnecessary suffering to Percy, a female white lion-head rabbit who belonged to distraught Rebecca Atkinson.
One of the 17-year-olds stole Percy from his hutch in Seaham, Co Durham, before taking him back to a house in the town.
Percy was seen on the film in the bath with the beer-swilling youths.
He was later shaved and hurled out of a window to his death.
The incident provoked outrage in the town with over 5,000 people signing a "justice for Percy petition."
The family was told about the video by friends who had seen it after it was posted on a social media site in June.
They could not bear to watch it, but were shown a screen grab of their pet in the bath, and the nature of the torture has been described to them.
Images of the abuse shocked hundreds of social media users who went online to show their disgust.
One, Rachel McNicholas, wrote: 'Vile vile vile. Even worse are the 59 people that's liked it. Hope its been reported to police."
Mrs Atkinson's husband, Anthony, said: "We only thought that Percy was stolen so we reported it to the police but we never even imagined that someone could do something like this to her.
"When she received a message showing her what happened to Percy we were shocked. It's disgusting and sick, what ever goes through people's minds?
"To torture an animal in that way and throw it out of the window is inhumane, we can't stop thinking about how much she would have suffered.
"We are all heartbroken. Rebecca and the kids cried all night and haven't slept."
Mrs Atkinson, 31, had only just bought Percy with her male rabbit companion, Ken, for her children Jessica Lennox, 14, Aaron Lennox, 10 and Brynn Atkinson, four.
Percy has left behind five 11-day-old babies who are now left without a mother.
Mrs Atkinson's daughter Jessica said: "I can't believe anyone could be so cruel."
The four youths admitted causing unnecessary suffering to an animal and one of the two youngest defendants admitted stealing Percy.
The case, heard at Peterlee magistrates court in Co Durham, was adjourned until the start of October for the preparation of pre-sentence reports.
(Mirror UK - Sept 13, 2014)
You four sicko Kuntz ought to die of dick rot with cancerous secondaries. That poor animal was worth more than the four of your sorry lives Put together and it's just a fkn shame your fathers' cum didn't land in your mothers' ugly fkn faces or better still on the floor. Shit suckers the lot of you
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