Only a 78th-minute try from Conrad Smith in the right corner gave the All Blacks a 15th successive Test victory and protected their 20-year triumphant run at their Auckland stronghold.
Lancaster accepted that England contributed to their own downfall with unforced errors and a lack of composure in the closing stages of a match that was there for the taking.
"There's frustration at having not got across the line despite having done so much good work to achieve a draw or potentially even a win," the head coach said.
"We created lots of opportunities. We made line breaks, broke the gainline. Our set piece was good, but it's fine margins.
New Zealand 20 England 15: Player ratings
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"The over-riding emotion in the changing room is frustration. What we must do as a coaching team is bottle that frustration and turn it into a positive mindset for next week.
"It definitely feels like we missed a chance. At 15-15 it's all about territory and how you manage and close out the game.
"We had opportunities to clear our line a bit and play in their half and put pressure on them.
"In tight games at 15-15 it's a drop goal or penalty that wins it. They got the penalty and tapped and won it.
"We're desperately disappointed having fought so hard to be in the game for so long.
"It's an 80-minute game and credit to them for closing it out. It was a tremendous effort and it's tough to not come away with anything."
Much of a desperately tight match was a battle of the boot, with the outstanding Freddie Burns and Aaron Cruden exchanging penalties, and it was not until the 71st minute that New Zealand were able to take the lead for the first time.
England threatened the line on several occasions and despite being hamstrung by a lengthy injury list and the absence of their Aviva Premiership finalists, who watched from the stands, were the equal of the world champions.
The performance bodes well for the remainder of the series, which continues in Dunedin next Saturday and concludes in Hamilton seven days later, but Lancaster admitted there is no more margin for error.
"We definitely need to win the next Test to win the series. It's a massive game for us because we always came into this series believing we can, but you must deliver," he said.
"The game next week is huge for us because we want to tie the series and go to a decider in Hamilton believing we can win it.
"They will have a similar side while I imagine we'll make a couple of changes. They will definitely improve, but we'll improve as well.
"We'll learn a lot from this game and we do that well as a team - we learn quickly."
Lancaster had no complaint with the late yellow card given to Marland Yarde for killing the ball but hinted at frustration with the general performance of referee Nigel Owens.
Arguably the key moment of the game was Cruden's brave decision to spurn a shot at goal for a tap penalty that ultimately led to Smith's try.
"It was one of those games where we had to take the match by the scruff of the neck. We needed to break the deadlock somehow," All Blacks head coach Steve Hansen said.
"There were two teams going at it hammer and tongs and Cruden did something different and that changed the game. I thought 'good on you son'.
"Now I hope you'll see what we've known all along and that's what a good team England are.
"It was a dour game and there were a lot of errors from both sides, probably down to rustiness. We have a lot of work to do between now and next weekend.
"We know now this will be one of those special Test series. We gave ourselves a mark of around 70 per cent. We'll probably have to be 30-40 per cent better next weekend."
PA
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