Foster said they felt he should have been allowed to return on their understanding of the laws.
There had been confusion amid the revolving door that was happening at the time with two yellow cards and the red card issued by referee Jaco Peyper.
Foster echoed the concerns of other international coaches when he said the game was in danger of being turned into a card festival, and had gone too far with its laws.
"There were clearly strong messages sent out last week. There was a feeling we should have had four yellow cards last week. And it seemed to be the mindset that went into this game," he said.
"If you look at our cards you have to look at them singly. We get the Leicester [Fainga'anuku] one, I think that's just incredibly unfortunate, but they're the rules. I don't think there's anything in that one.
"Ofa [Tu’ungafasi] we accept and Angus [Ta'avao] we accept, I think most people could see a change in direction, a big prop reacting and a collision that's pretty unfortunate," he said.
Foster said on Sunday the disappointment lingered and the result gave him flashbacks to the 2017 British & Irish Lions series and the red card to Sonny Bill Williams. On that occasion the All Blacks showed a lot of attitude and tried hard but like on Saturday night, they weren't good enough.
"We hate losing, it was a game with a whole lot of twists and turns, and things happened, but we just weren't good enough in that second half against a 15-man team," he said.
At the same time, he said, while there was doom and gloom in the All Blacks' camp, the results across the southern hemisphere had been good for world rugby and it set next weekend up well.
The All Blacks had to get better and there had to be questions resolved about why things didn't go better for them in the game.
"That's a normal process, the trouble is when you lose it sounds like you're sulking. We've just got to keep clarity on the equitable side of how the game is being officiated," he said.
There was no doubt the All Blacks wanted the win. The end of the first half showed that when down to 12 men for moments and massive commitment and attitude and problem-solving skills to score their try, which he felt should have seen a penalty try before first five-eighths Beauden Barrett's try.
Facing 40 minutes one man down in the second half, Foster felt the side's 'hands got hard'.
"Sometimes when you get a bit tense, and you want it too much, you start to snatch at the ball, and there was some collision work and handling errors that showed how much we wanted it but not quite the smarts to trust what we do," he said.
It was a case of extreme circumstances facing them ahead of the third Test in Wellington but they had to show they had learned from the Dunedin experience. They hadn't become a bad rugby team overnight, he said.
Foster felt the side has advanced on last year and didn't get what they wanted from Dunedin.
"I don't think it's a true reflection of where we're at, but it's a true reflection of Test match rugby," he said.
Ireland are a fantastic side and two top teams had gone head to head which was fantastic for the All Blacks, Foster said.
There would be extra pressure around the Wellington Test but that was what top rugby was all about.
"If we can actually climb the mountain this week, and really grow what we started at Eden Park, then we can still finish this campaign in a really good spot," he said.
"We've got some growth to do, we've got some players who are learning quick, and there's no room for error when you're playing Ireland and you've got a couple against South Africa. This is what this team needs right now. I know it's hurting but we'll get there," he said.