"It was important that we just didn't let them get away from us, they (Scotland) batted well and got some good shots away," Allen added.
"But as the game went on, the rate went up, which resulted in wickets falling."
Calum MacLeod top-scored for Scotland with 33 as New Zealand went 1-0 up in this two-match series.
Wednesday's encounter was Scotland's first match since a damning report found Cricket Scotland, the national governing body, to be "institutionally racist".
The report, which found 448 examples of institutional racism, was commissioned by sportscotland, the national funding body, last year after Scotland's all-time leading wicket-taker Majid Haq and former teammate Qasim Sheikh said they had suffered racist abuse.
Prior to the report being made public, the entire board of Cricket Scotland resigned.
Haq and Sheikh met with stand-in Cricket Scotland chief executive Gordon Arthur on the sidelines of Wednesday's match.
A Cricket Scotland spokesperson said Arthur had a "very constructive discussion" with Haq and Sheikh, explaining he had "apologised for the time it has taken to get to this stage and the impact it has had on them and their families".
The spokesperson added: "They have agreed to meet within the next week and have a shared commitment to ensure cricket in Scotland is a truly welcoming sport with equal opportunities for everyone."