Warne, revisiting a theme he favoured during Australia's 3-0 Ashes defeat in England last summer, has suggested the tourists may well be about to lose the urn unless Cook changes his ways.
But Jonathan Trott cited England's success on home soil under Cook as counter-evidence to the opinion of Australia's record-breaking wicket-taker.
"To win 3-0, I don't think the tactics were that bad," Trott told Sky Sports News.
The number three batsman also believes that appearances can be deceptive, and many outside the England team are mistaken about Cook's methods and capabilities as a leader.
He said: "I know there are people who think he is inept at it, but everyone in the changing room knows he's well ahead of most people in that department."
Pace linchpin James Anderson and vice-captain Matt Prior also defended Cook.
"He leads by example, and just drags everyone with him," said Anderson.
Prior added: "There is always going to be scrutiny and the captain as a leader is always going to come under fire.
"But Cooky's a very strong person mentally.
"He takes it all in his stride, and ultimately his record speaks for itself. He's doing pretty well."
Warne had blasted Cook ahead of this winter's Ashes series and questioned his style of captaincy.
The former Australia leg-spin bowler, who is now at home in the commentary box, laid into the England captain during the Durham Test, just before Stuart Broad kick-started a collapse which gave the home side outright series victory for a third successive time.
Revisiting one of his favourite subjects before the first Test at The Gabba, Warne told national newspapers: "He can be negative, boring, not very imaginative - and still win and be happy.
"But I'll tell you my opinion - I think Alastair Cook has to be more imaginative.
"I think if Australia play well, and he continues to captain the way he does, England will lose the series.
"He lets the game drift."
Warne also singled out 22-year-old England opening batsman Joe Root for criticism.
Warne, a cornerstone of Australia's Ashes dominance in the 1990s and 2000s, thinks Root needs to be given a break down the order at number six.
The former leg-spinner's preference to replace the Yorkshireman alongside Cook is his own former Hampshire team-mate Michael Carberry.
Root's first series as an opener was only a qualified success, despite his second-innings 180 in England's landslide Lord's Test victory over Australia.
"If I was choosing the side I'd open the batting with Carberry and put Root down to number six," said Warne.
"Root played really well at Lord's, and Australia had a bit of a shocker there.
"But I don't think he's an opener. I don't think his technique is tight enough. He will be found out opening in Australia."
Warne senses Australia have the pace to severely undermine Root on their own bouncier pitches.
"I think you could be crucifying him if you're facing Ryan Harris or Mitchell Johnson on fast, bouncy pitches," he said.
"He's going to 'nick off' a lot and I think - as we saw before, aside from Lord's - Australia really did have his number."