Former opener Matthew Hayden also took aim at Cummins, criticising the field placements after Kohli's arrival in the middle.
Nathan Lyon walked into the record books with career-best figures of 8 for 50 as India suffered another batting debacle.
'It's unfair to disrupt the balance of the team just to accommodate a big-name player who is out of form.'
Australia are already without another regular all-rounder in Cameron Green, who was ruled out of the India series after opting to have surgery on a stress fracture in his lumbar spine.
Australia completed a six-wicket victory within two days in the first Test against South Africa on Sunday as the Proteas crumbled on a green Gabba wicket that played straight into the home bowlers' hands.
Australia bowled out Sri Lanka for 231 in the hosts' second innings and then chased down the target of 75 losing the lone wicket of opener Travis Head.
A Mitchell Johnson bouncer that struck India captain Virat Kohli on the helmet during the first Test on Thursday might actually help players get past the shock of Phillip Hughes's death, according to Australia spinner Nathan Lyon.
Images from Day 3 of the first Test between Australia and India in Perth on Sunday.
Aiden Markram himself knows what he is capable of -- and how to express it on a cricket field. And South Africa will be the biggest beneficiary in the coming years.
Australia's opener Matt Renshaw tests positive for COVID-19, will feature in Sydney Test against South Africa
Australian cricket legend Ian Healy is shocked by the team management's decision to include two off-spinners -- Nathan Lyon and young Todd Murphy -- who have almost similar action.
IMAGES from Day 1 of the opening Ashes Test played between England and Australia at Edgbaston in Birmingham on Friday.
Australia spinner Nathan Lyon said there is no room for racial abuse in sport and hailed India pacer Mohammad Siraj for calling out racial abuse during the recently-concluded third Test in Sydney.
Patel smashed 74 and dominated his 114-run partnership for the eighth wicket with Ashwin to rescue India
Former Pakistan leg-spinner Mushtaq Ahmed feels the categorisation of Test and limited overs spinners is the need of the hour. According to Mushtaq, skill-wise, Lyon and Ashwin are on par with greats like Saqlain Mushtaq and Muttiah Muralitharan but not best suited for the one-day game.
At Stumps on Day 3, the visitors are struggling at 51/4 with right-hand batter KL Rahul (33*) and team skipper Rohit Sharma (0*) unbeaten at the crease.
Australia's assistant coach Daniel Vettori said he does not mind the spin-friendly pitches on offer in their series in India as they have challenged the batsmen and brought their skill and perseverance into play.
Jaiswal and Rahul ended the day unbeaten on 90 and 62, as the hosts failed to take a wicket in two sessions, a dizzying change of pace from day one when 17 wickets tumbled.
Happy to chat with Kohli, buy him lemonade off the field, says Lyon.
Ravichandran Ashwin becomes leading wicket-taker in Border-Gavaskar Trophy history
Rohit has joined an upbeat Indian team for the last two matches and Lyon is aware of the threat the batsman can pose with his wide range of strokes.
India's Abhishek Sharma has surged to the second spot in the ICC Men's T20I Player Rankings for batters after a stunning 135-run innings in the fifth and final T20I against England.
He is the ninth bowler and fifth spinner to complete the feat in Tests.
Images from Day 3 of the second Test between Australia and South Africa at the Melbourne Cricket Ground on Wednesday.
Australian batter Marnus Labuschagne described wicketkeeper-batter Rishabh Pant as the most "amusing" player in the Indian team, ahead of the upcoming five-match Test series between the fierce rivals.
Ravichandran Ashwin became the first bowler to pick 50 or wickets in each of three World Test Championship cycles.
Alongside the experienced Nathan Lyon could play rookie Todd Murphy, who is yet to play an international match.
Fast bowler Jayden Seales produced a record-breaking spell to put West Indies in command on Day 2 of the second Test against Bangladesh.
Smith needs just 315 runs to become the fourth Australian batter after Ricky Ponting (13378), Allan Border (11174), and Steve Waugh (10927) to reach the landmark of 10,000 Test runs.
Both Pant, who played a key role in India's series victory last time, and Carey are known for their aggressive brand of cricket.
Nathan Lyon is pleased to have bagged the prized wicket of 'head of the snake' Virat Kohli.
Indian batting stalwart Virat Kohli and Australia's Steve Smith would be more than keen to stamp their authority in the upcoming Border-Gavaskar series in which runs would be "at a premium", feels Australian great Matthew Hayden.
Australia spinner Nathan Lyon termed Indian players as superstars' while hoping to revive his on-field rivalry with India spinner Ravichandran Ashwin.
Australia's pacemen Mitchell Starc and Pat Cummins ripped out England's top order with a masterclass of textbook bowling to put their side in sight of a 2-0 Ashes lead on Saturday.
Eoin Morgan said the current Indian team ranks as "one of the greatest in their own conditions".
Australia Test captain Pat Cummins expects greater workload with the ball for all-rounders Cameron Green and Mitchell Marsh against India
Ricky Ponting slammed the current team for showing 'no desperation'
Australia's star-studded bowling line-up showered praises on Pakistan's star batter Babar Azam, with a handful of them labelling the right-handed batter as a "class player".
Ashwin acknowledged the emotional turmoil he was experiencing, despite his calm demeanour.
Steve Smith has said he had never encountered a wicket like the one at the SCG