The Black Caps, who had lost the toss and were sent in to bat, made a solid start but could only muster 153 for eight in their 20 overs as England restricted them to just 20 runs in the last four overs.
England easily reached their target after opener Jason Roy bludgeoned 78 off just 44 balls to give the Three Lions a good base to work from and they cantered to victory with almost three overs to spare.
Williamson said after the game: “We were 130 for three, which certainly is a very good platform in any match that you play in T20 cricket.
“We couldn’t capitalise on it. It is such a small part of what you look at when you [look for things to] improve on. It would have been nice if we had got a few more there.
“It wasn’t due to lack of effort, and England bowled well. It’s one of those things. Twenty20 is very fickle in nature, and today wasn’t meant to be for us.”
It was another exit at the semifinal stage for New Zealand in a major tournament but Williamson said the nature of T20 cricket is such that if you have a bad day the opposition will win.
The Kiwis came into the last four clash with a perfect record in the tournament having won four from four, having beaten India, Australia, Pakistan and Bangladesh, but Williamson insists that his team did not feel the pressure of the game.
Williamson said: “I think every cricket game you play you look at it as an isolated event. You accept that when you turn up to the ground you want to play your best cricket, but if the other team plays better then you tend to come second.
“That’s what happened to us. We didn’t win. We didn’t play the better cricket. England were very very good. As simple as that.”