Captain John Barclay lamented “one that got away” after Scotland missed the chance to beat the All Blacks for the first time in their history.
The Scots fell 15-3 behind and then 22-10 with 13 minutes left but Huw Jones’ late try gave them hope of an upset.
Stuart Hogg’s break almost saw him go over in the left corner in the final play, but New Zealand held on to win.
“We are gutted we lost that game. I am very proud of the effort but I think it’s one that got away,” said Barclay.
“You don’t get too many chances [to beat the All Blacks] – because of scheduling, injuries, non-selection – and I think we have let one get away, which is disappointing.
“But we have to look at the positives. This is one of the best teams in world sport, not just rugby, let’s not forget that. What we have done is pretty good but hopefully we can finish the job off next week against Australia.”
Barclay, winning his 65th cap, said he thought it was “the loudest I have ever heard Murrayfield”, the crowd sensing the prospect of history in the making as Hogg raced for the corner in the last seconds.
“How good is he?” Barclay said of Hogg, who was named man of the match. “It is scary. He was outstanding tonight and his attacking play has been outstanding for the last couple of years. He is a very valuable player for us.”
Hogg, for his part, insisted Scotland “firmly believed” all week they could beat New Zealand, and came agonisingly close to backing up that claim.
“We were on the brink of it weren’t we?” he told BBC Sport. “We were very, very close to getting that. Credit to our boys, I thought we were outstanding for the whole game.
“We were aware of how tough the challenge was going to be, and we have just come up short. You don’t get to play the world’s best on many occasions and to come up short is bloody disappointing.
“We made a couple of mistakes here and there which allowed them back into the game, but jeez, we can take some confidence from that and fire into Australia next week.”
Scotland head coach Gregor Townsend declared himself “very, very proud” of his side.
“The way we defended in the first half, and the way we played a lot of rugby in the New Zealand half was a great starter for us,” he told BBC Sport.
“But I thought the way we attacked in the second half, we built a lot of pressure, created opportunities, lots of penalties and yellow cards.
“The spirit and courage we showed from our 22 at the end to almost get in at the corner, it would have been a perfect day.
“When it was on to go wide, I thought Stuart was going to go in. It wasn’t to be but it was a fantastic effort.
“Stuart was outstanding. Considering he missed the first three months of the season injured, he has come back well with Glasgow and today he dominated in the air, he was on the ball a lot and he was very hard to defend against.
“The confidence we will get from that performance will do us really well over the next few months and hopefully seasons.”
Townsend revealed that prop Darryl Marfo and replacement flanker Luke Hamilton had both suffered ankle injuries, while Hamish Watson, Zander Fagerson and Alex Dunbar were also forced off during the game.
“We will have to find out how serious they are in the next couple of days,” Townsend added.
New Zealand coach Steve Hansen paid tribute to the Scottish performance, as he praised his own players’ “incredible resilience”.
“We were under the cosh for long periods but the players have got a lot of self-belief in themselves and they showed that,” he said.
“Scotland have beaten Australia and they are a good side. I thought they were outstanding today.”
Analysis – Former Ireland & Lions captain Paul O’Connell on BBC TV:
“I think it is an opportunity lost for Scotland. They should have won that game. They had so many opportunities.
“Their line-out gave them a great platform but their scrum let them down. When they were attacking five metres from the line they didn’t create like New Zealand did.
“That was a big weakness in the Scotland side today.”