Cook has been faced repeated calls to resign the captaincy from the likes of Michael Vaughan and Nasser Hussain during a run that has seen England go 10 Tests without a win.
Meanwhile Cook's form with the bat has also declined.
It is now 27 innings since he scored the last of his England record 25 Test hundreds, and the left-handed opener's last nine Test innings have yielded just 129 runs.
At the time, the ECB cited the need to support Cook's captaincy as a reason for ditching Pietersen.
And the South Africa-born batsman said a fear of being seen to go back on that decision was the key reason why Cook was still captain.
"At the moment only politics are keeping Cook in a job because the England and Wales Cricket Board backed him so much that it would be yet another PR disaster if it sacked him now," Pietersen wrote in his Daily Telegraph column published Saturday.
"He (Cook) should do what is right for England and resign the captaincy. He has shown he does not have the tactical brain to lead the side," said Pietersen of the 29-year-old Essex batsman.
"England badly miss Cook the opening batsman scoring 150 to set games up at the top of the order and, relieved of the captaincy, I don't think it is too late for him to rediscover this form."
"Cook needs people with experience of international cricket around him, which (England coaching team) Peter Moores and Paul Farbrace lack.
"Look at Marvan Atapattu working with Sri Lanka, Rahul Dravid with India, Shane Warne with Australia.
How many ex-international players have England had recently working with them? None. There is so much knowledge in English cricket going to waste.
"There are so many great cricket brains in the Sky studios. Put that radio in your ear, listen to them on the balcony or in the dressing room and Mike Atherton, Nasser Hussain, Warne or whoever could be saying something you didn't know and could implement in the game.
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