Scotland captain Preston Mommsen says his side caused New Zealand "some jittery moments" during the Black Caps' three-wicket win in Dunedin.
Mommsen was one of four Scots out first ball but Matt Machan and Richie Berrington hit fifties to help the qualifiers from 12-4 to 142 all out.
New Zealand lost seven wickets in the run chase before sealing victory.
"Two wickets in two balls changes it completely, and we would have been sniffing victory," Mommsen said.
"There were some jittery moments for them towards the end of the game.
"Overall, I am pretty proud of the performance, especially the fight and the character we showed in the second half."
Berrington and Machan put on a stand of 97 for the fifth wicket, but Scotland's batting challenge faltered after the pair departed in the space of eleven deliveries.
"Richie and Matthew feel disappointed that they got in, got a great partnership going, but then failed to get a big one," he continued.
"However, I think they showed the skill and the quality we are capable of."
New Zealand, who now head Pool A with two wins from their opening two fixtures, showed an attacking mindset as they chased down the target with 25.1 overs to spare,
"Potentially they changed the way they played, in chasing a low total, to get their net run rate up," Mommsen acknowledged.
New Zealand skipper Brendon McCullum admitted his team's rather frantic reply tarnished some outstanding bowling from the seamers.
"It was a really good performance with the ball - with the bat, we showed glimpses but we have to improve," he said.
Next up for the co-hosts is a day-night encounter in Wellington on Friday against England, who lost heavily by 111 runs in their opening match with Australia in Melbourne.
"England will be a challenge - they're hurting," McCullum added. "They'll be tough to beat and we'll have to play incredibly well."