New Zealand didn't qualify for the next round, so there is definitely something wrong with them. We didn't find the New Zealand team in the few matches they left in the beginning because the New Zealand team is not such a performing team. Maybe it was because this was the first time New Zealand played in American conditions that they did not perform as expected.
I would not agree with your point of view that because New Zealand did not played before in the United States, they lost the matches. If we see that this is the first time any ICC event is held in USA, so the pitch and conditions are new for every team. It is just how these teams react to the situation and adapt the situation.
Talking about the New Zealand's journey, they lost both of their initial matches with Afghanistan and the West Indies. Although they won the last two matches against the smaller teams (Uganda and P.N.G), but that does not matter much. Well they can say that if they had the matches with smaller teams first, then they could have idea about pitches and perhaps show a better performance against big teams. I think these are just excuses and New Zealand has to admit that their performance was not up to the mark in this WC.