"If we could have managed to score 20 to 30 runs more than we did it would have been different," he told reporters. "We were very close, a few runs short but very close."
New Zealand put themselves under pressure by losing six wickets in quick succession to give Mashrafe hope, but the contest was ultimately decided by Bangladesh's failure to take their chances in the field.
Kane Williamson should have been run out for eight, but the Kiwi skipper was reprieved by wicketkeeper Mushfiqur, who dislodged the bails with his arm, and went on to build a 105-run partnership with Ross Taylor that put New Zealand in control.
Mashrafe refused to criticise Mushfiqur for his mistake but was left ruing the missed opportunity.
"If you don't score big you have to take all your chances," he added. "Mushi, I don't think we need to go after him. It could happen to anybody because he was also trying hard to get him.
"He wants to pick the ball and suddenly it hits his elbow. Those sort of mistakes always happen on the ground."
The result leaves Bangladesh sixth in the standings ahead of their next match against England in Cardiff on Saturday.
Former ODI spinner Abdur Razzak said his countrymen would not be daunted by the prospect of facing the favourites given their World Cup record against England, who Bangladesh beat at the 2011 and 2015 editions of the tournament.
"These are different teams... but there is a lot of confidence from those wins," Razzak wrote in a column for the International Cricket Council.
"(Bangladesh) may not necessarily win but they will certainly give them a good game. England have more pressure... and we've beaten them in our last two World Cup matches."
(Reporting by Shubham Kalia in Bengaluru, additional reporting by Rohith Nair; Editing by Simon Jennings)
