She was tending the animal in a field in Garsdale on Friday, when it is thought the animal became frightened and stood on her chest, police said.
The Air Ambulance flew her to the Royal Lancaster Infirmary but she died later that day in the operating theatre.
Cumbria police have investigated the matter and have said there were no suspicious circumstances.
A spokesperson for the police said the girl suffered "severe chest injuries which were life threatening".
The matter is to be passed to the Coroner.
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