India skipper Virat Kohli backed Ajinkya Rahane despite the veteran batsman's dry spell and absence from Monday's thumping second Test win over New Zealand, promising his team will support past performers.

Rahane, who led the hosts in the drawn opening Test and managed scores of just 35 and four, missed the final game due to a hamstring niggle as Kohli returned from a break to take his place.

The 33-year-old has averaged under 20 in 12 matches this year and his injury pull-out was judged by Indian media as a respectable way to drop him in Mumbai.

"I can't judge his form. No one can judge it. Only the individual knows what he's going through," Kohli told reporters.

"We need to back them in these moments, especially when they have done well in the past. We don't have this environment where we have our players asking 'what happens now?'."

Kohli said the team was unaffected by outside criticism of individual performances.

"We support everybody in the side, Ajinkya or anyone. We don't take decisions based on what happens outside," he added.

'Good year', 'good headache'

India won the second Test by 372 runs to clinch the series 1-0 in Mumbai.

Kohli said his team were flying high despite losing the world Test championship final to New Zealand in June and failing to reach the T20 World Cup semi-finals last month.

"The year has been very good for us, we have played very good cricket. There were two setbacks in T20 World Cup and World Test Championship," he said.

"Victories in England and in Australia gave us a lot of confidence. See, the Indian team is expected to win everything but that's not realistic, we know what we need to work on and improve on and look forward."

Opener Mayank Agarwal was named man of the match in Mumbai for his 150 and 62 in India's dominant batting show.

The team is currently brimming with young talent including Shreyas Iyer, who sparkled on debut in the first Test with 105 and 65 to make his case in the long-format team.

Fast bowler Mohammed Siraj took three wickets in the Black Caps' first innings, while off-spinner Jayant Jadav returned career-best figures of 4-49.

"It's a good situation to be in, we've had injuries in the lead-up, so we need to manage our players physically and mentally," said coach Rahul Dravid.

"It's going to be a large part of my challenge. Challenge too for the selectors and the leadership group. It's a good headache to have."

India now travel to South Africa for three Tests starting December 26 followed by three one-day internationals in a tour shortened by worries over the new Covid Omicron variant.