This latest loss came hot on the heels of a 103-run thrashing by world champions Australia.
Lara's men have now lost both their first two matches in the second phase of the tournament and face an uphill task in qualifying for the semi-finals
West Indies selector Andy Roberts, during the New Zealand match, gave an interview on local radio saying the five-man panel as whole had, since February, no say in the make-up of the team.
The comments from the former West Indies fast bowler came amidst suggestions that only Lara and coach Bennett King were currently picking the side.
"Bennett King is best to answer that," Lara told reporters after Thursday's match.
"I think we picked the best team possible. I can simply say to Andy Roberts that I did not select this World Cup team. I was not there at the meeting.
"The team was selected without me but I still go out there and fight my best with the 15 players (World Cup squads are 15 strong) given to me.
"Everybody has West Indies' interests at heart and if people want to be critical at this point in time, I don't think it's fair. We just have to try to play to the best of our ability and get to the semi-finals."
New Zealand captain Stephen Fleming was among those surprised by the omission of fast bowler Jerome Taylor, which meant the West Indies attack had just one genuine quick in Daren Powell, on a pitch Lara had labelled a "batting paradise" after the Australia game.
"We were scouting for three seamers playing but we were able to get best use of the pitch and our boys bowled incredibly well," Fleming said.
But Lara, after seeing West Indies bowled out for 177, said batting, not bowling, was the team's biggest problem.
"We haven't scored 250 runs yet in any of our games at the tournament," said Lara.
"The significance of game against Kiwis was in scoring 177. You can have 10 bowlers and you are not going to defend it.
"We've just got to look at where we are going wrong - on this track we've lost our top order twice and today it was 81 for four. We are putting the rope around our necks.
"If we are going to perform then we need one of the top three or four batting through and getting a score."
Lara added there was only so much he could do as captain to improve the batting.
"You can't pat people on their backs if they are not doing well. You've got to look at the mistakes and correct them.
"We didn't play to our full potential and the guys have to be told that."
But Lara, whose 37 against the Black Caps was surpassed only by opener Chris Gayle's 44, said a lack of patience with the bat was proving costly.
"I just think on a couple of occasions guys got set and we didn't go on - Chris Gayle was looking good, (Ramnaresh) Sarwan and all of a sudden in a matter of three or four overs we had lost wickets.
"I think maybe the guys are not looking at the fact we've got 300 balls to face."
Lara, asked if he was batting himself too low at No 5, said the likes of Marlon Samuels, who'd made great play of batting at four following a hundred against Kenya in a warm-up match, had to produce in the tournament proper.
"If we are going to win the World Cup it's not going to be on the back of one or two of them or myself, it's got to be the entire team," said Lara, again disappointed with another meagre crowd at the Sir Vivian Richards Stadium.
"We've got to get into the frame of mind of winning everything from now on. This is really a desperate time."
West Indies' next match is against Sri Lanka in Guyana on Sunday.