The All Blacks were in a class of their own at Tokyo Stadium, Aaron Smith claiming a quickfire first-half double and Beauden Barrett also crossing to put the holders 22-0 up at the break.
Codie Taylor, Matt Todd, George Bridge and Jordie Barrett touched down in the second half, with Ireland having to wait until 11 minutes from time for Robbie Henshaw to go under the posts and get them on the board before they were awarded a late penalty try.
New Zealand will face England in a blockbuster semi-final next week and Best was full of praise for Steve Hansen's men after they sent him into retirement on the back of a hammering.
"The All Blacks were fantastic tonight. We felt we prepared well, we felt we had a game plan, we felt we have enough in our armoury to beat them, but they came out of the blocks hard at us, put us on the back foot and like good sides do, they never let us off that again," Best said.
"I think they were just really, really clinical. They didn't let us get on the front foot and this is a front-foot, momentum game, especially in knockout rugby.
"The boys who are here will have to look back at this and see how they can get better, but right now you have to give enormous credit to the All Blacks - they were fantastic tonight."
Best was given a huge ovation when he was interviewed on the pitch after the match and the 37-year-old expressed his gratitude to head coach Joe Schmidt at the end of his reign.
"I've loved every minute of it," said Best. "The support that I've got from fans when we are at home and away, my team-mates, the coaching staff and public and in particular Joe, who is moving on.
"I think he brought Irish rugby and probably my game to a different level and a lot of credit and a lot of thanks must go to him."