Several New Zealanders checked on Kohli and helped him stretch his hamstrings when he went down with cramps while scoring a century to help India romp to a 70-run victory at the Wankhede Stadium and a place in Sunday's final.
Former Australia all-rounder Simon O'Donnell slammed the Black Caps for their lack of competitive instinct but Mitchell, who scored a 119-ball 134 in New Zealand's response, said the approach would not change.
"I think that's something we really pride ourselves on as Black Caps and as New Zealanders. We want to play cricket in a way that suits us as a country and how we want to see our kids grow up and play the game themselves," he told reporters before the team left Mumbai late on Thursday.
"We'll keep playing cricket the way we do as Kiwis and hopefully the rest of the world can respect us and how we go about our day-to-day life, not only on the field but off it as well.
"It's something that we're really proud of, so we'll just keep being Black Caps and doing what we're doing."
New Zealand next travel to Bangladesh for a two-test series starting on November 28 and Mitchell said the disappointment of their semi-final exit at the World Cup would not have any impact on their performance.
"That's the nature of international sport these days," he said. "(After) the T20 World Cup final we played a couple of years ago, we had a T20 in India about 48 hours after that so we're used to it.
"We'll show up, we love test cricket, it means a hell of a lot to this group. We'll be ready to go come the first day of that test and wear that black cap again."
