Australian captain Tim Paine apologised Tuesday after launching an ugly tirade at India's Ravi Ashwin in the drawn Sydney Test, admitting he was "bitterly disappointed" in his own conduct.

Paine said frustration got the better of him on Monday when he tried to unsettle Ashwin, who played a key role as the tourists denied Australia to salvage a draw on the final day of the third Test.

"I want to apologise for the way I went about things yesterday... my leadership wasn't good enough, I let the pressure of the game get to me," the Australian skipper told reporters.

Stump microphones picked up Paine making a series of verbal jabs at Ashwin, including calling him a "dickhead".

But the tail-ender was defiant and his unbeaten 39 helped keep the series level at 1-1 to set up a winner-takes-all fourth and final Test in Brisbane starting Friday.

Paine acknowledged his actions undermined the goal he set himself when appointed Test captain in 2018 to revamp the team's toxic culture after the "Sandpaper-gate" ball-tampering scandal.

"I'm a captain who wants to enjoy the game, who wants to play the game with a smile on his face and I fell short of my expectations and our team standards," he said.

Paine, who was also fined for dissent after an expletive-laden rant at umpire Paul Wilson on day two of the match, admitted "my mood throughout the whole Test was probably a bit off".

He insisted the behaviour was a "blip" that would not be repeated and said he had not considered standing down as captain over the incident.

Critics, including former England captain Michael Vaughan, said Australia appeared to be heading "back to the old days" of sledging and foul language.

Star batsman Steve Smith, who was Australia's captain during the sandpaper cheating scandal, also attracted negative attention when footage suggested he scuffed up batsman Rishabh Pant's guard at the crease.

The stump camera showed Smith shadow batting and then apparently rubbing off the pitch marks -- made by the batsmen to judge where they stand -- with his boots.

Paine said it was just part of Smith's regular routine. 

"It's one of his mannerisms, he was marking centre, he wasn't by any stretch of the imagination trying to change guard or do anything like that," he said.

Paine dropped three catches during the epic final day, including a chance from Ashwin shortly after their exchange, which did not help his mood.

"I ended up looking the fool didn't I? You open your mouth and then you drop a catch," he said.

He said he spoke to Ashwin after the match and they joked about the mistake.