The former foreign secretary accused the Supreme Court of exceeding its power in ordering that the so-called "black spider memos" be released.
The 27 letters reveal the prince expressing concerns to then PM Tony Blair and other Labour ministers.
A 10-year government battle to keep them secret was declared unlawful by the Court of Appeal and Supreme Court.
Despite having helped to write the Freedom of Information (FOI) Act under which the memos were published, Mr Straw told the BBC he was "very much on the side of those" who said they should have been kept secret.
He said it was "absolutely essential" that Prince Charles had been able to offer his views in private, adding that if the public was entitled to know what he was saying it would "stop him saying anything at all to ministers".
The former Labour minister, who was suspended from the Parliamentary Labour Party at his own request in February after facing cash-for-access accusations, has heavily criticised the FOI Act since helping pass the bill in 2000.
He said: "Although the Freedom of Information Act, for a variety of reasons, was in its conception and execution a bit of a dog's breakfast, Parliament was absolutely clear that there should be protection for this kind of correspondence, and if necessary the attorney general could be given the right of veto.
"One of the really worrying aspects of this case which has not received enough attention is that the Supreme Court, on a split decision, decided in their wisdom to literally rewrite what parliament had decided."
The "black spider memos" - named after the appearance of the Prince's handwriting  - were published after a decade-long campaign by the Guardian.
They reveal that the prince wrote to Labour ministers to express his views on a wide variety of topics, including historic buildings, herbal medicine, healthy food and the plight of the albatross.
Campaigners have welcomed the publication of the letters. Graham Smith, chief executive of anti-monarchy campaign group Republic, said they revealed the prince's "meddling" with government business.
Former Labour Environment Secretary Dame Margaret Beckett said the release was "unfortunate".
"If he had known his letters were going to be published he might have couched them in different terms," she said.
Jack Straw has criticised the publication of private letters sent by Prince Charles to government ministers.