By the time gun spinner Ish Sodhi found his rhythm, knocking over match-winner Jason Roy (78 off 44) and Eoin Morgan in consecutive deliveries in the 13th over, it was too little too late.
"Yeah it didn't look like spinning much so you're trying to skin it as best you can," said Williamson.
"They certainly got off to a very good start, they played really nicely. Jason Roy had an outstanding game and certainly took the game away from us in that second innings.
"But at the same time we're conscious of playing the long game, which is pulling the game back, which we managed to do and put a little bit of pressure on them.
Colin Munro talks to the Crowd Goes Wild Breakfast:
"You get a couple more wickets on that and all of a sudden you're right back in the game but it wasn't to be today and credit to England for the way they played, the way they bowled in their death overs and the way they came out and took the contest away from us."
Roy punished New Zealand seamer Corey Anderson for four boundaries in five balls in the first over, and from there England were like a runaway train.
However, Roy denied Williamson had played into his hands by not hitting him with his bowlers of the tournament Sodhi and Santner in the opening exchanges - instead arguing that England had gained the benefit of winning a crucial coin toss.
"I don't know, (New Zealand) are an extremely smart side. They've got through this tournament with flying colours and credit to Kane," he said.
"It was one of those wickets where balls seemed to swing a little bit for us and then the cross seamers were holding in the pitch a little bit. But I think the pitch almost got a bit better (for the second innings) and it slid onto the bat a bit more (for England's batsmen).
"Their plans are their plans and I wouldn't ever say that it was a stupid idea."
New Zealand got off to a rapid start thanks mainly to Williamson (32 off 28) and a sensational innings from No.3 Colin Munro who blasted 46 off 32.
But through the middle overs, England suffocated their opponents with Chris Jordan and Ben Stokes leading the way with the ball, and New Zealand ultimately could manage little more than a run-a-ball for their final 10 overs.
Anderson, Ross Taylor, Santner, Luke Ronchi and Grant Elliott swung for the fences but could never find the boundary rope.
Williamson said the platform set by the top order after losing the toss and being sent in was evidence that this was no semi-final choke by his previously unblemished side.
"No I don't think so. We were 130-3, which certainly is a very good platform in any match that you play in T20 cricket," he said.
"We weren't able to capitalise ... it wasn't through lack of effort, England bowled well.
"It's one of those things. Twenty20 is pretty fickle in its nature and today it wasn't meant to be for us."
The way in which England virtually put the run-chase in the bag with in the first four overs had Roy claiming his side had played as close to the perfect match as possible.
"It's pretty cool. After the first game it was pretty far away. It's something that we're really buzzing for. It's going to be an incredible experience and we can't wait," he said.
"That's a pretty special (knock) for me. It wasn't just me - the bowlers were outstanding towards the end and their skills were amazing. I'm just hugely proud to be involved.
"Today was as good as it probably gets in winning a T20 game."
- Sydney Daily Telegraph
