Greatbatch slammed his players, saying they "aren't as good as they think they are" following the 0-4 ODI series defeat in Bangladesh and that some of the batsmen had inflated opinions about their abilities.
Mills said he had not received any player reaction to Greatbatch's comments but he felt they would take it on the chin.
"Paddy (Greatbatch) is an emotional guy, he cares passionately about New Zealand and the Black Caps and I know he is as gutted as anyone else at the results in Bangladesh," Mills said.
"It's been a difficult time and a lot of people have been rightly upset about the performance. There is always going to be some harsh words spoken, so I think everyone's got to focus on being constructive and getting the job done in India and getting the team back performing where it can," Mills was quoted as saying by 'Dominion Post'.
Greatbatch, who is the New Zealand batting coach, did not single out anyone but the comments appeared to be directed at the top order batsmen.
"It was inexcusable to lose 4-0 to Bangladesh. When you play badly like that you've got to front up. It's very devastating. We played like dicks, really, and I suppose there's one positive thing, we've got a chance next week to actually put it right," Greatbatch had said.
"I think some aren't good enough. I think some think they are better than they are and the third one, I think, is the mind," he said.
New Zealand's Test squad has little time to prepare in India, with no warmup match before the first of three Tests starting in Ahmedabad on Thursday.
Former international and now commentator Craig McMillan said warm-up game should have been included when the tour was arranged.
"You can have four days of nets but it's not the same as batting in the middle and playing in a game situation. They're going to be up against it, no doubt about that," McMillan said.