While England had two late chances to edge the All Blacks, only for first five-eighths replacement George Ford to hit a post with a penalty goal attempt and then miss a dropped goal in the final act of the game, Savea said rugby was a game of fine margins, and they would take the 'w' [win].
"To be honest that game could have gone either way. If that kick had gone over we could have been the ones with our heads down."
However, after knocking on the ball after the penalty goal attempted rebounded off the post he was proud of the defence the All Blacks mounted to hold their lead.
England's tackling throughout the game had been punishing.
"They were bringing line speed in, putting big shots on us, and we just had to smile it away and keep going.
"It was a game of back and forth but we're glad to get the win."
The front row played their part in the final scrum as England looked to set up Ford for his dropped goal attempt.
"That's a testament to our front row. A lot of work has gone into that. The loosies were aware of the drop-kick so had to try and do two jobs. You know those are big moments and we won that one in the end."
Savea said the All Blacks wanted to see space and try to play hard against England's line speed.
It was a risk, but the risk was a reward for the All Blacks.
"There were times that it didn't go well, but there were times that it paid off. That's the kind of footy we want to play, see space and just jam."
England coach Steve Borthwick said, "We gave them a window to get back and they took it. We were in a position to win that game. You've always got to respect the opposition. That New Zealand side are a quality side who have played seven Test matches and been together for three months. It's a different context to where we're at."
Captain and hooker Jamie George said, "Whenever you put yourself in positions like that and don't come away with a win, then you're going to be disappointed.
"We learned lessons from the summer and certain games that have been close in the past and the bounce of a ball, a kick goes slightly further left and we're talking about a different result."
George said they couldn't blame Ford because he had landed plenty of kicks during his career.