Joe Schmidt feared that Ireland would be denied victory in a repeat of 2013, his first outing against his native country as Ireland head coach.
Ireland won 16-9 in a nailbiting finale after Jacob Stockdale's stunning set-piece try gave Ireland the crucial lead.
"It was a heck of a battle. The All Blacks are so tough to beat. I had visions of 2013 as they worked their way back up the pitch," said Schmidt on RTÉ2.
"But our guys kept their discipline really well and kept within the system towards the end when we had to.
"We had a couple of really positive attacking moments - one of which we scored off. A super try from Jacob Stockdale, a super finish."
He thought Ireland might have held onto the ball for longer in the final two minutes.
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"I felt maybe we could have kept the ball at the end but it wasn't a bad thing to keep it nice and close to the touchline and try to keep them pinned in their own 22.
"We had to fight really hard at the end.
"As a collective team, they're all pretty relieved."
He added that maintaining Ireland's winning record at the Aviva Stadium was a key motivation for the team.
"This is our home. This is two years we haven't been beaten here and we wanted to keep some pride around that.
"You should've seen the Shelbourne Hotel when we came out. There were people so deep supporting the team. The Fields of Athenry tonight, the support of the crowd.
"We were incredibly conscious that we wanted to deliver for those people and I really felt in the nature of how we had to work tonight, we did that."