Sussex Police applied to the High Court for copies of the interviews, alongside results of tests on aspects of the accident. Both requests were refused.
However, footage filmed by onboard cameras was handed over.
A Hawker Hunter plane crashed into spectators and motorists on the A27 in August 2015, killing 11 people.
Det Ch Insp Paul Rymarz said the force was pleased the court had granted access to "some of the material" it was seeking for its investigation.
"We understand that legally this case is without precedent in England and Wales and we accept the reasons why our request has not been granted in full," he said.
"We remain committed to finding answers for the families and friends of those who died."
Sussex Police applied to the High Court for the disclosure of records, which are given a protected status in law, in July.
Lord Chief Justice Lord Thomas and Mr Justice Singh refused the application earlier, except in relation to the film footage from within the aircraft.
Mr Justice Singh said the footage had "significant potential value" for the police investigation.
A spokesperson for the AAIB said: "The AAIB is not able to release protected air accident investigation records of its own accord. Only the High Court can allow for their release.
"We note today's judgment and will now release the film footage to the chief constable of Sussex Police."
Police have been refused access to interviews carried out with Shoreham air crash pilot Andy Hill by the Air Accidents Investigation Branch (AAIB).