New Zealand scored 241 for eight and England were bowled out for 241 off the last ball of their 50th over, leaving the match tied. Both teams scored 15 runs in a Super Over and England won the trophy because they hit more boundaries in the match.
"I don't know how they won it, was it boundaries or something?," Williamson said.
"Gutted, the guys put in a huge effort to get this opportunity, to pretty much do all you could and still not get across the line," he told a news conference.
England were struggling in their chase and benefited from a huge slice of luck in the final over when a New Zealand throw-in hit Ben Stokes's bat and went to the boundary.
"A couple of uncontrollables today that are pretty hard to swallow but we take nothing away from England today and through the tournament they are deserved winners," Williamson said.
New Zealand were happy with the total they posted after electing to bat on a pitch which was tricky to score quickly on.
"We knew 250–260 wasn’t easy to get, you saw in the first 10 overs the movement, we were able to pick up some early wickets. Our bowlers were putting ball in great areas," Williamson said.
New Zealand lost in the final for the second World Cup in a row after finishing runners-up to Australia four years ago and their wait to lift the trophy for the first time goes on.
"The thing you walk away with is the amount of heart the guys have put in during the whole campaign and today," Williamson said.
"While it's raw it's pretty hard to swallow – two teams worked really hard to get to this moment – two attempts to separate them. But it is what it is – the rules are there and nobody probably thought it would come to that.
"It was a fantastic game to be a part of so it's hard to look at it in a rational way at the moment - - but it was a great spectacle for everyone," added Williamson, who was named the player of the tournament after scoring 578 runs.
"It’s not about individual accolades, the whole squad has put into the bucket and that’s always the focus," said Williamson, who left the room to a warm ovation from the assembled reporters.
"One of the great things about the game is that on any given day pretty much anything can happen and we saw that today."
