Visiting captain Steve Smith hit the only century of the match in Pune after being spilt four times by the butter-finger hosts who were thumped by 333 runs inside three days in the spin-dominated contest.
Smith's 109 allowed Australia to set India an improbable target of 441 to win the first match of the four-test series and the hosts duly collapsed.
"We had a chat about it and we are working on few of the areas where we could have done much better in the last test match," Vijay, who spilt one himself, said ahead of the second test beginning on Saturday.
"We are looking forward to this game and hopefully we can pull of those catches."
Having conceded a 155-run first innings lead, India badly needed to restrict Australia in the second but poor catching allowed the visitors to post 285 and effectively bat the hosts out of the contest.
"The first innings lead was little more than what we expected. From there on it was always going to be tough for us to get into the game," Vijay said.
"We had the opportunities, if we had taken those catches maybe we would have put lot more pressure on the Australians.
"But it didn't happen and we got to take it in our chin and move forward."
The defeat snapped India's 19-test unbeaten run, shocking fans who expected the team to steamroll Australia.
Vijay said it was a challenge for his team to show their character and bounce back in the remainder of the series.
"We have lost the game and we have to accept that fact. We have to move forward," Vijay said. "We are looking forward to this game and start fresh... We will look to put the pressure back on the Australians.
"It's going to be a good challenge for us as a team and test our character. That's why we are playing cricket and hopefully we can play the way we have to play and we have played before."
(Reporting by Sudipto Ganguly in Mumbai; editing by Amlan Chakraborty)
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