Emily Gardner, 14, from Gloucester, was on board the boat when it was overturned by a large wave in waters off Brixham, Devon, in May 2015.
Her "ill-fitting" buoyancy aid snagged on a cleat, trapping her underwater.
A jury recorded a narrative conclusion at an inquest in Torquay. The coroner said it was "the most tragic incident".
In a statement, Emily's family said they planned to campaign for new legislation to ensure power boat drivers required a licence or training.
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They said they wanted it to be known as "Emily's Law" to prevent others having "to endure what we have been through".
After the hearing, they also called for all buoyancy aids to be "fitted safely and correctly".
The two-day hearing heard the boat was driven by co-owner Paul Pritchard, who said he did not see the large wave or he would have taken evasive action.
Emily was taken to hospital but pronounced dead after 80 minutes of resuscitation attempts, the hearing was told.
Following the hearing, her father, Clive Gardner, said: "My family and I miss Emily so, so much, and time will never heal. Our lives are ruined. Our hearts are truly broken and will never mend."
In a statement, the family also said that "if we had known that power boat drivers do not have to have a licence or training we would never have let her go".
They added: "We need people to become aware of the absence of legislation to ensure the safety of passengers on leisure craft, and will campaign for laws to be brought in to close this legal loophole."
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