Chasing 349 for a win at the Manuka Oval, the visitors were sailing along at 277 for one before they lost nine wickets for 46 runs to nosedive to 323 all out in 49.2 overs.
Losing the match by 25 runs, India trail the five-match series 0-4 and Dhoni was expectedly disappointed.
"I am not angry, I'm disappointed. This was one game we should have batted much better. I'll take responsibility, I should have carried on but I got out...There was a bit of pressure on the youngsters. International cricket is all about pressure, you think about the right shot. You realise you have to take a bit more time and take the game slightly to the end," Dhoni said in the post-match presentation.
"Rohit batted very well with Shikhar. And Dhawan and Kohli batted majestically. In the last five years, we have not had a fixed bowling line-up other than the spinners. That pushes us to the extreme to get some extra runs," said Dhoni.
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On a roll, Australia skipper Steven Smith not only praised the effort of Dhawan and Kohli, but also gave full credit to Richardson and his team's never-say-die attitude.
Richardson registered his maiden five-wicket haul in ODIs to earn a well-deserved Man of the Match award and he was over the moon.
Kohli said that the team would continue to do what it has been doing in the fourth and final Test at Dharamsala.
Australia skipper Steven Smith termed Marsh and Handscomb's match saving partnership as 'resilient'.
"A pretty good Test. Proud of the way the boys stuck it out. That's what we want to be...Resilient. They played beautifully today. They didn't look like they would get out for a while. It was crucial for us, at such an important time. It was important to score big first-innings runs, we left ourselves a bit short there. 450 was not enough to win this match," said Smith.
"Maxwell was sensational. That's the way we want him to play. Pat Cummins, in his first game in a very long time, he bowled beautifully. Not too often you spend 210 overs in the field. It was a long two days. The boys really dug deep. I am really proud," he said.
Smith said his team was looking forward to Dharamsala.
"Massive game in Dharamsala, can't wait to get there," he said.
Man of the match Pujara said he never thought that he would play out as many as 525 deliveries, which he faced during his double-century knock.
Pujara also said that his and Saha's partnership was "much-needed for the team".
"They scored 450, to come back, go past that total, and put them under such pressure was great. But Shaun Marsh and Peter Handscomb batted really well," he said.
"You get fatigued, but I have been working hard on my fitness, careful with my diet, and hoping to recover soon for the big Test coming up," concluded Pujara.