"We haven't showcased our ability as we know we can and there are guys in that dressing room determined to come back strong".
To that end, a pair of boundaries from Billings to begin the 18th over was a good start but he was caught off Billy Stanlake (2-28) from the next ball and when Kane Richardson (3-33) had Buttler caught on the rope from the last ball of the innings, England were 137-7.
The injury could prove to be a major blow for England with team doctors yet to make a call on whether Morgan will be available for the New Zealand leg of the series. Both sides are looking for their first win in the series. We were determined to show what we are capable of and we didn't do that, ' said Buttler, deputising as captain for the injured Eoin Morgan.
They may have to do so without Morgan, who was a late scratching at the MCG due to what was described as a groin niggle.
Tim Southee captained New Zealand to victory over Pakistan at their last visit to Westpac Stadium last month.
The grounds in New Zealand are smaller though the surfaces can sometimes be tricky to score on so England will need to adjust quickly.
David Warner produced some shrewd fielding to run out Dawid Malan as Australia secured back-to-back victories over England in the tri-nation T20 victories on Saturday.More news: Plane carrying 71 people crashes near Moscow
More news: Newcastle rock Man Utd as Huddersfield win at last
More news: VLC 3.0 brings Chromecast support and many others new features
"Losing three early poles, I felt the best way was to then to take some balls and kick on at the end, but that never really happened", he said.
Wellington's Westpac Stadium will host a rare Tuesday night worldwide between the Black Caps and England.
"We didn't quite soak up the pressure early on with the bat and then we never really kicked on. I'll have to improve and look at where I went wrong".
It was a second drubbing for England after going down by five wickets to Australia in Hobart on Wednesday.
Australia's Glen Maxwell (L) and D'Arcy Short congratulate one another during the Twenty20 International Tri-Series cricket match between England and Australia at the MCG in Melbourne on February 10, 2018.
New Zealand re-assemble with similar concerns to England over their middle order after three successive T20 defeats, with two new faces Mark Chapman and Tim Seifert summoned to address it.