Australia are 1-0 down in the five-Test battle for the Border-Gavaskar series after being crushed by a record 295 runs at Optus Stadium.
Cummins said Australia were still a "really tight unit".
"There's plenty of times where the batters have dragged us bowlers out of tight situations and we've done the same," the Australian quick said.
"It's probably one of the tightest teams I've ever played with.
"We really enjoy playing cricket together.
"We've been through a lot the last few years, the core group.
"So no problems there. Everyone gets along really well, so all good."
Shastri, who coached India to victories on their last two tours of Australia, was stunned when he heard comments from Josh Hazlewood saying he was already turning his attention to the second Test before the Perth match was over.
Hazlewood fronted the media after day three when Australia were in complete disarray at 3-12, chasing a record 534.
The No.11 was still required to bat on Monday.
"What the Indian dressing room will be thinking when they hear something like that is we know there are some cracks on the pitch, but there are some mental cracks as well in the opposition," Shastri said on Fox Cricket on Monday.
"Having come to Australia for 30-40 years, I think this is the first time an Indian team is feeling that, you know what, 'We're better than the opposition', in their own backyard.
"I don't think an Indian team has ever thought that way.
"Quietly at the back, they're thinking, 'We'll have to lose it from here ... if we stick to what we're doing well, and execute properly then we have the upper hand'."
Josh Hazlewood had figures of 1-28 off 21 overs during India's second innings in Perth. (Dean Lewins/AAP PHOTOS)
Former England captain Michael Vaughan also said he was "staggered" by Hazlewood's comments.
"Publicly, I've never heard an Australia come out and divide the camp as batters and bowlers," Vaughan told Fox Cricket.
"To publicly see a player basically say, 'I'm thinking about the next game before this game has finished' ... I've never, ever seen that from an Australian player."
