But Cummins defended the selections after the match.
"We were confident it was our best XI this week," Cummins said. "We know the quality Trav is. He's a huge part of this team but we were confident in the 11 guys out there. He's been really good around the group. He's been out the back working really hard on his game like he always does."
Starc was unavailable for the first Test in Nagpur having suffered a finger tendon injury in the Boxing Day Test in December. He has been bowling regularly over the last month despite the injury but remained in Sydney until he was available to play.
Hazlewood and Green are with the squad but both were ruled out of the opening Test. Hazlewood has been battling Achilles tendonitis. He had a solid centre-wicket bowl on Wednesday and then had another bowl in the centre on Saturday morning before play but has not pulled up as well as he needed to in order to be available in Delhi. Green remained an unknown for Australia as he continued to recover from a broken finger he suffered in the Boxing Day Test. He has been batting and bowling but Australia could well be cautious with him despite desperately needing his all-round skills to balance the side.
"Starcy lands today or tomorrow into Delhi," Cummins said. "I think Joshy might not be quite ready for Delhi. He's getting up and running now, he's pretty close, but I don't think he'll be quite ready for Delhi. Greeny's a bit of a wait-and-see. We're still hoping. He's had a couple of good hits out here. His bowling is pretty good, so over the next couple of days we'll assess it."
Cummins was quite calm about the nature of the defeat. He didn't appear concerned at all that Australia had capitulated by an innings for the second consecutive Test on the subcontinent.
"I think sometimes it's almost easier to put those kind of losses behind you," Cummins said. "You are looking at small margins. You have to have a hard look at your game and the big strides you need to change to give yourself the best chance next week.
"We've had a really good run the last 12 months. There hasn't been many losses in that change room. I don't think we need to reinvent the wheel. It's just tweaking different approaches to how we play and maybe particular methods."
Australia will remain in Nagpur and are likely to review and recover over the next two days before ramping up their preparations for the second Test once they arrive in Delhi.