England went into their game with New Zealand in Wellington having suffered two defeats to the Baggy Greens, but a 12-run setback against the Black Caps has left the tourists on the brink of finishing in last place.
Alex Hales and Dawid Malan scored 47 and 59 respectively in England's total of 184-9, but Buttler says that he and his teammates gave their opponents too much of an advantage as New Zealand posted a target of 197.
The stand-in skipper is quoted by BBC Sport as saying: "Maybe we gave away 10 or 15 too many. We were just off with our skills and the wicket played better than everyone thought. We did not bowl as well as we could have. We dragged it back pretty well at the end.
"We got a fantastic start. When Alex Hales is in that form, he rivals anyone in that powerplay. Dawid Malan impressed as well and we needed them to extend it further. We did not get the cameos in the middle either.
"We need a favour from Australia to beat New Zealand - we will see what happens."
Australia face New Zealand on Friday, before England play the Black Caps for a second time two days later.