Barrett's dropped goal and another penalty edged New Zealand ahead, but it had to endure a nervous wait after England flanker Sam Underhill took advantage of a charge-down and sprinted 30m down the left wing for a try with four minutes left.
Thriving in the wet, England went up 15-0 at one stage through a try from Chris Ashton, drop goal from Co-capatin Owen Farrell, a penalty from Elliot Daily and a further try from other co-captain Ben Hartley, and looked set to knock over the travelling All Blacks.
His team regrouped and full-back Damian McKenzie scorched over the line before fly-half Beauden Barrett converted and added a penalty, as New Zealand narrowed England's lead to 15-10 at half-time.
But they reduced England's lead to two points when Barrett landed his maiden Test drop goal before a second penalty nudged the All Blacks in front for the first time in the match.
Asked how England would prepare for Japan, Jones said: "Sushi and sake!"
The scrum-half lofted a long, high ball and it gave Ashton just enough space to speed to the corner, sliding in as an embarrassed Rieko Ioane failed to recover in time.
New Zealand almost caught England cold right at the start of the second half after a jinking McKenzie sliced his way through before linking with Ben Smith and Aaron Smith only for wing Rieko Ioane to drop the scrum-half's pass when a try was in sight.
"We're taking it seriously and that's why we have to be absolutely ruthless about the game", he said.
"In tough conditions it's tough to get our game going, so we're hoping and praying for a bit of weather".
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"Sometimes the game loves you, sometime it doesn't".
Adding to England's frustration is that at last week's World Rugby-organised gathering of officials and coaches to discuss key areas of the game, the revised TMO protocol was outlined.
Reflecting on the match as a whole, former Australia and Japan coach Jones said: "We're obviously devastated". Generally speaking, he is going well, but we want more actions from him.
"Allowing Jonker to make the final decision would also seem to contravene the directive that requires "compelling evidence" for the TMO to intervene with World Rugby considering Lawes to have been marginally offside".
"They are the best team in the world at the minute and have been for however many years".
"There was no doubt [Lawes] is offside".
"If we'd kept going for another five minutes, we maybe would've got them". Hartley found Itoje from the line out and the England maul drove perfectly, aided by everyone, over the line and Hartley only his third global try, this time his fellow co-captain added the extras. We had opportunities to win the game, we didn't take them, they did so they deserved to win the game.
"Because that's what happens when you play New Zealand sometimes - you sit there and you watch and you think "they're the best team in the world, we can't compete against them".