The England coach has seen his side bowled out for fewer than 200 at the start of their last four series, most recently in the drawn first Test with New Zealand in Dunedin.
England also got off to sluggish starts in series against Pakistan, Sri Lanka and India, and Flower has said that he will examine the issue.
"The way we started this tour, principally in that first innings, has nothing to do with people not having enough cricket," he told Sky Sports News.
"We've had a reasonable amount of preparation time, and enough to get ready for that first Test. So that is not the reason why we under-performed.
"I have some ideas on rejigging a couple of things in our preparation, in our management team firstly, and we'll see if we can do something about it.
"We always encourage our players to be honest with themselves, and each other. So then we've got to do the same. The coaches have to do that, and I'm the first guy that has to do it."
England's second Test against New Zealand begins in Wellington on March 14.