Freya Thorpe, 4, was playing on September 8 when it happened in Upper Heyford, near Bicester in Oxfordshire.
She was rushed to hospital but died two days later, Oxfordshire Coroners' Court was told.
A passer-by found her and called 999, but medics were unable to save her life.
She had been playing with a friend when it happened.
A GoFundMe appeal set up after Freya's death has raised more than £21,000 for her family.
A police investigation concluded that Freya had slipped on the bark of the tree.
Her father, Chris, told a packed inquest room, full of relatives and police, that he was grateful for the support people had showed his family.
The communications company director, who was the proud father of young 10-day old twins when Freya died, told the inquest: "I would like to thank every single person who tried to assist my little girl.
"Me and my wife loved her more than life itself. We are doing our best to survive."
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