He said Ireland was using a cut-and-paste attack with no variations, which assisted the All Blacks in efficiently maintaining patience.
"It was hard to get your nose in; we were hunting and searching, but we showed patience.
"With Scott McLeod and Joe [Schmidt] helping him, we have been building our system for today and how we wanted to defend. We are making some strides in that space, and I was delighted.
"One mistake and the game could have gone the other way. But you haven't been to a World Cup if you haven't had a game like that. I remember the South Africa [semifinal] game in 2015. That is what World Cups are about – you've got to roll your sleeves up and trust what you do."
Foster said it was a special day.
"The world has been talking about these two quarterfinals for 12 months, even longer. France v South Africa is likely to be the same. They are massive games, two very proud teams, desperate to win it.
"Sometimes the sweetest victories are when your opponent plays really well and test you to the limit. We didn't want to play Ireland with two yellow cards. We played a lot of that game with 14 men but I couldn't be more proud of the players. I thought we looked in control of it."
After injuries forced some changes, Foster said he was pleased that the combinations they fielded for the game were made for the type of Test they played.
"Ardie [Savea] was outstanding again, he put his body on the line, and Shannon [Frizell] brings a different style to the game. He was running on empty at times a bit but the loosies [loose forwards] played well. It was a bit stop-start in the second half, it just meant we could keep our combinations intact for deeper into the game. I still felt we were in control for large parts of it."
Second five-eighths Jordie Barrett's denying Ireland a lineout maul try when getting under the ball was a big moment.
"The other big moment was when we were under a bit of pressure; we had a defensive lineout and scored 80 metres up the park. That was a big moment in that second half because there is something about scoring long-range tries that can deflate a team, and that put us out to eight points and set the platform for it.
"The nice thing was the mix of some really good attacking stuff and some really courageous defensive stuff."
Foster said they had emerged from under the radar for the remainder of the tournament, the first step of which is playing Argentina in a semifinal on Saturday [NZT]. The loser of that game will play the bronze medal match against the other semifinal loser.
Foster had sympathy for Ireland. They had built a team to break their quarterfinal bogey and had high expectations.
"We have been there as a team; we know what that's like. We know some things kill you in those situations.
"Our role was to be quiet and steel ourselves for the challenge. We know Argentina well, and they know us well. It will be a heck of a game – a southern hemisphere game.
