England, who had already retained the Ashes, won the fourth Test at Chester-le-Street by 74 runs on Monday with more than a day to spare to take an unbeatable 3-0 lead in their five-match series against arch-rivals Australia.
The tourists, needing 299 to win, were well-placed at 120 for one at tea.
But an extended final session saw Australia collapse spectacularly to 224 all out, with England fast-medium bowler Stuart Broad, who took six wickets for 20 runs in 45 balls, doing the bulk of the damage on his way to Test-best match figures of 11 for 121.
Leg-spin legend Warne, the first bowler to take 700 Test wickets and regarded as a shrewd tactical thinker during his playing days, said Cook had been far too defensive early in Australia’s second innings.
“Cook was way too cautious at the start of Australia’s run chase,” Warne wrote in Britain’s Daily Telegraph newspaper.
“He had a deep point, would move slips out as soon as there was a good shot through the covers and the bowlers were bowling too short and not full and at the stumps.”
Warne added Cook, who has lost only one Test in his 12 matches as England captain, was too reliant on England head coach Andy Flower and the team’s Australian bowling coach, David Saker.
“Saker and Flower knew England were losing the Test largely because of the captain’s approach but the tea interval came at the right time for England.”
While commentating on television, Warne criticised Cook’s decision to bring on Tim Bresnan in the final session, only for the Yorkshire seamer to claim the key wicket of well-set Australia opener David Warner, who made 71.
Flower said Tuesday that Cook deserved credit for that move.
“He made some decisions that turned the game… bringing on Bresnan, who got Warner straight away,” Flower told reporters.
England off-spinner Graeme Swann, the leading wicket-taker in the series with 23, also said Cook’s critics were wide of the mark.
“I know there are people saying he is too negative but I stand next to him in the field at second slip and know what goes on in his mind — he is very calculating,” Swann was quoted as saying on Wednesday by The Sun tabloid.
“He is both aggressive and defensive when he needs to be. That makes him an excellent captain.”
Meanwhile Warne’s former Australia team-mate Glenn McGrath said there was a hint of the old “Baggy Green mentality” in the current England team.
“The Australian team that I was lucky enough to play in had a certain aura and sometimes you had teams beaten before you walked on the field,” McGrath, Test cricket’s most successful fast bowler with 563 wickets, wrote in British daily The Guardian.
“England aren’t at that stage but after 12 Tests without defeat and five wins in six they’ve got that confidence, that belief.
“We saw something of that old Baggy Green mentality from England on Monday evening. When you’re playing in a good team where you’re confident in yourself and your team-mates, when you’ve done the business before, it makes it so much easier,” added McGrath, who like Warne retired from Test cricket following Australia’s 5-0 whitewash of England in 2007.
“The opposite is also true: when you’re used to losing you somehow keep finding ways to lose.”
The fifth and final Test of the series starts at The Oval in south London on Wednesday, August 21.