The north London club decided not to offer the Welshman a new contract earlier this season and he subsequently agreed to join Serie A table-toppers Juventus in the summer.
And Crouch, who moved to Burnley in January after eight years with Stoke, has questioned the piece of business by the Arsenal hierarchy.
Writing in his weekly column in the Mail, the former England striker said: “It’s another week that has shown the error of their ways.
“I have written a couple of times this season about Aaron Ramsey and you will know my position.
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“I found it madness they were not prepared to offer him another deal and I can’t believe they are losing him to Juventus for free.
“Ramsey is quality. He is the type of footballer that should cost someone £40million in a transfer fee alone.”
Crouch also believes Emirates chief Unai Emery will find it difficult to replace Ramsey, just as they have done with Alexis Sanchez following his move to Man United last season.
“If Arsenal want to replace him like-for-like, that is the type of investment they will need to make, along with top-end wages,” he said.
“They will find it is no straightforward task.
“For Arsenal to make the same mistake so soon after losing Alexis Sanchez has left me scratching my head. It was avoidable.”
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