The injured juvenile bird was found by walkers near Errwood Reservoir, in Derbyshire, on 5 September and taken to a vet in Ashbourne.
The bird died under anaesthetic while being X-rayed. Post-mortem tests showed it had been hit with shotgun shot.
Sarah Fowler, chief executive of the Peak District National Park, said she was "appalled" by the incident.
It is believed the shooting could have taken place about six days before the bird was found.
Ms Fowler, who was speaking on behalf of the Peak District Bird of Prey Initiative, said: "This case shows what we are up against in trying to reverse [bird of prey] fortunes.
"It is incredibly difficult to catch someone in the act or to collect evidence and make a case for prosecution."
Sgt Darren Belfield said persecution is a "problem" in some of Derbyshire's upland areas with offences taking place away from public view in isolated areas, often in the early hours of the morning.
There have been a number of incidents of raptor attacks within the Peak District this year.
In April, footage emerged of a man apparently trying to attract a protected hen harrier with a decoy bird on National Trust land in the Peak District.
Derbyshire Police were unable to secure a prosecution but the incident led to the trust terminating a grouse shooting lease on its land for the first time.
The force said recent surveys showed seven sites in the Peak District were occupied by peregrine falcon pairs and one by a single juvenile female in the Dark Peak area of the park. Two pairs have bred successfully this year.
Police are investigating after a peregrine falcon died after being shot in the Peak District National Park.