The singer – who was in Portugal at the time of last week’s search – has denied an alleged sex crime against a boy at an evangelist event at a Sheffield stadium in 1985.
“I think anybody not charged should not be named by the police, and shouldn't be reported in the newspapers either in my view,” said Parkinson on ITV News.
“I think the Cliff Richard case only highlights the feeling there is some kind of witch hunt going on.”
The veteran journalist criticised the BBC’s decision to cover the search without any charges or arrests having been made.
“I think the BBC did create an error in judgment, not in understanding the story and having the story and trying to follow it through, but in reacting to the story in a kind of way that would have done the red tops credit,” continued Parkinson.
"That's what wrong with the BBC, I think, on this one. It was the manner in which they chose to actually cover the event – if you can call it an event.
Cliff Richard: Life in pictures
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“I think there is a lot to be looked at and a lot to be learned from all that's been happening around that particular kind of area.”
Parkinson noted that in the case of Rolf Harris (who was imprisoned for his sexual abuse crimes) the media arrived at his Bray home before the police.
“It's not right. Particularly at that point, he was not charged with anything,” he said.
"I just feel that they should tread more softly and we should be more considerate of everybody's feelings and claims and rights in this.
“We should pursue people, of course, who have done wrong. That is indisputably the police's job.”
Richard’s family also defended the singer this weekend.
“I know my uncle is innocent,” said his niece, Linzi Jolin, while his cousin, Garth Gregory, described the raid as a “witch hunt”.
