Vunipola, who has 43 caps, echoed their coach's words and the 26-year-old is wary of an in-form Wallabies side who are unbeaten in seven games.
"We have to look at the game, see where we can improve and take the learning otherwise... Australia (given) the team they are at the moment and the form they're in at the moment, they'll take you apart," Vunipola told British media.
"We're going into it with a new slate, new opportunities to perform better than we did and we know Australia will be a tough opponent and one we're looking forward to.
"We know we've got areas to work on. But the important thing was coming out, getting the win. We know we were rusty in certain elements."
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Vunipola identified a lack of discipline as a major problem for England who are ranked second in the world behind New Zealand and have won 20 of their 21 tests under Jones.
"You've got to take the learning from it, you can't brush things under the carpet. There were some good bits as well. I think we defended pretty well," he said.
"Unfortunately our discipline wasn't too great in allowing them out too easily. And as a team that's something we've got to address. But all in all a good first hit out, with much work to do."
England also host Samoa on Nov. 25.
(Reporting by Aditi Prakash in Bengaluru, editing by Ed Osmond)
