Dean Price went into the River Esk at Longtown after his seven-year-old daughter, Delilah, slipped and fell into the water on 30 June.
The 32-year-old, from Walsall, got into difficulties and disappeared. His body was found hours later following an extensive search of the river.
The South Cumbria coroner recorded a verdict of accidental death.
Geoff Maxwell, an off-duty retained firefighter who was working nearby, managed to rescue the girl.
He was praised by coroner David Roberts, who said: "On behalf of the public generally, I would like to thank you for your selfless act."

Chris Parker, 33, of no fixed address, was charged with two counts of theft on Tuesday.
He was remanded into custody following the hearing at Manchester and Salford Magistrates' Court.
Mr Parker was previously reported to have comforted a seriously injured girl and a woman who died in his arms.
He was charged with stealing a purse and contents from Pauline Healey, whose 14-year-old granddaughter Sorrell Leczkowski, from Leeds, died in the explosion.
Mr Parker is also said to have taken a mobile phone from a different teenage girl.
He will next appear at Manchester Crown Court on 13 September.
Twenty-two people died in the attack at the end of an Ariana Grande concert on the evening of 22 May.

Ryan Craig Preston, 23, was also accused of drink driving, failing to stop for a uniformed constable and failing to report an accident.
He was arrested after a 22-year-old man was struck by a car as he left the EQHQ nightclub in Livingston on Saturday.
The victim was treated in hospital but his injuries were not thought to be life-threatening.
Mr Preston was also charged with failing to give police his name and address and other details.
A Crown Office spokesman said Mr Preston, from Kirknewton, West Lothian, made no plea or declaration during his appearance on petition at Livingston Sheriff Court.
He was committed for further examination and released on bail. The date of his next court appearance has not yet been set.
A man drowned while trying to rescue his daughter from a river in Cumbria, an inquest has found.
[NEXT_CONCEPT]
A man who was hailed a hero after the Manchester Arena attack has denied stealing a bank card and mobile phone at the venue on the night of the blast.
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A man has appeared in court charged with attempted murder after an incident outside a West Lothian nightclub.