The Kiwis went into the match as favourites, as the only remaining unbeaten team in the tournament.
England, by contrast, were defeated by West Indies in their opening game before securing wins over South Africa, Afghanistan and Sri Lanka.
Colin Munro (46) gave New Zealand a strong start, powering them to 89 for one at the halfway stage before Eoin Morgan's side took control with some smart catching and tight bowling.
New Zealand managed only 64 runs in the final 10 overs and 20 from the last four sent down by Chris Jordan and Ben Stokes.
"We got off to a good start but we were 20-25 short," Williamson told reporters. "England bowled really well in that death period which made life very difficult.
"Unfortunately we were not able to connect as well as we'd have liked. It certainly was not through a lack of trying."
For a team packed with big-hitters, New Zealand could not press hard enough on the accelerator pedal as England claimed regular wickets.
"We were 130 for three (in the 16th over) which certainly is a very good platform in any match if you're playing T20 cricket and we were not able to capitalise on it," added Williamson.
(Editing by Tony Jimenez)
