The Indians were given a day off on Wednesday, meaning their only training session between Melbourne and Sydney will be an optional one on Thursday.
Friday's fifth Test looms as doubly crucial for India, with a win needed to retain the Border-Gavaskar Trophy and keep their World Test Championship hopes alive.
But it is also important for Rohit's future.
So bad has his form been this summer there are genuine question marks on whether India's captain will even be in the team at the SCG.
The right-hander is yet to pass 10 in any of his five innings this series, with the run of failures also coming off the back of a poor showing against New Zealand.
Rohit Sharma has been dismissed by counterpart Pat Cummins in four of his five innings. (James Ross/AAP PHOTOS)
It would be a bold call from India's chief selector Ajit Agarkar to push for the 37-year-old to miss in Sydney, given Rohit's status as captain.
But his batting has become an issue, particularly with Shubman Gill left on the sidelines in Melbourne.
Kohli is also enduring a rotten run, his unbeaten 100 in the second innings in Perth now sitting alongside scores of 5, 7, 11, 3, 36 and 5.
In all six of Kohli's dismissals he edged balls outside off stump, while Rohit has fallen victim to his opposing captain Pat Cummins in four of his five innings.
But Carey said it would be wrong to suggest Australia's bowlers have a mental edge over the pair.
"I don't think I can put it that way," Carey said.
"You could also make that argument for a Steve Smith or a Marnus (Labuschagne) against Bumrah early.
"Champions of the game find ways to come out and perform, and they are champions. We have to be on our toes to not let them back into the series."
Beyond Rohit and Kohli, India's batting appears far more formidable with Yashasvi Jaiswal showing signs of recapturing his promising best in Melbourne.
The 23-year-old's crucial fourth-innings dismissal continues to remain as a sticking point, after replays showed a clear deflection off his gloves and into Carey's hands.
The absence of a spike on snicko has since prompted BCCI vice-president Rajeev Shukla to claim Jaiswal was "clearly not out".
Rohit admitted after the final-hour loss Jaiswal was likely out, but claimed India "more often than not" were on the wrong side of technology when it is not 100 per cent.
But Carey said he knew immediately Jaiswal had hit the ball.
"I had no doubt. I think the evidence was really clear that the third umpire made the correct decision," Carey said.
"Snicko has been a bit funny this series, so with all the evidence you get, you put it all together and I think the third umpire did a great job."
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