He was guilty of one card when taking down a maul and said players need to look hard in the mirror and improve their accuracy in those plays.
While sitting out his 10 minutes in the sin bin, he felt the pain of not being able to help.
"But at the same time, you've got to come on and bring composure, energy, the right sort of energy the boys need.
"I'm proud of the boys. We could have gone either way, with the crowd in the background. We could either take a breath and move towards that pressure, with what the Scottish were bringing to us, or we could be calm and then nail our next moments, and next moments.
"I thought we did that towards the end."
Savea said that being 17-0 up at halftime, the All Blacks knew Scotland would throw everything at them, which they did, and there were parts of the game where the New Zealanders didn't handle it.
"It's on us when we are in the lead like that to ask how we can be more ruthless because we weren't proud."
It felt like they were sitting in the press conference after a loss, rather than celebrating a win.
"In rugby, you're never satisfied, or we're never happy with a performance, but to come out of that, and the special occasion it was for Murrayfield, as All Blacks under the pressure we were, we're grateful and happy."
All Blacks coach Scott Robertson acknowledged replacement fullback Damian McKenzie's role in ensuring the All Blacks remained on track for their goal of a Grand Slam.
"You need someone that's clutch, and he's pretty mercurial. He can kick a 50:22, score a try and kick that penalty.
"You know he's going to inject something, and he did with his timing and his skill set. He's tough, and he trusts himself. We're pleased he did it again, and over and over.
"But you've still got to create it. We went in at halftime, and we were pretty clear what we needed to do, but dropped the kickoff, and 20 minutes later, we were under a lot of pressure.
"It was a proper Test match."
Playing with three yellow cards, the All Blacks were proud that they maintained their defensive effort.
"There were some amazing efforts on defence. We could have just rolled over and given up on one of the efforts, but we didn't. We stayed in it for such long periods, and when we needed to turn it over, [we did] and that's what we're really proud of.
"It wasn't perfect, the execution wasn't perfect."
Robertson felt that when the All Blacks held the ball, they looked good, and when they gained momentum, they retained it, which was what got them home.
