Foster said about their three one-point wins in the playoffs that the Springboks showed they had learned to fight in a dark place.
"They just know their game. They are strong, experienced. They've got the ability to play the game at their pace."
In a game dominated by the red card to captain Sam Cane and a let-off for Springboks captain Siya Kolisi for a similar offence, Foster said the use of the TMO was something for the game to think about in the future, not on the night of the final.
"We got the same behaviour from that TMO that we got in the Irish series last year, same TMO. So we expected what we got."
He congratulated South Africa for the tenacity they had shown through the tournament.
"For us, it's heart-breaking, and I look at the effort of our team. We gave ourselves a really good chance in that second-half, especially after the damage that red card created."
Foster said he didn't want to be talking about red cards. There would be a time in the future to analyse that.
"The game has got a few issues it's got to sort out. That's not sour grapes. There were two similar incidents, one was a red, one was a yellow."
He said both sides had chances in the pressure cooker environment.
"To get ourselves back, score that try; it's disallowed, and we get another try. We gave ourselves every chance, but it wasn't to be.
"We are all gutted. We so desperately wanted to win this, but I am equally proud. The attitude to play against a mighty team. We contributed massively to a final which had a lot of drama."
Foster defended his captain, Cane, and said he was a worthy All Blacks captain.
"I am incredibly proud to coach him. It's a tough old day at the office when that [red card] happens, and he'll be feeling a lot of emotion."
Cane said he was feeling so much hurt and was struggling to find the words to explain it.
"I am so proud of the group the way they fought back and gave ourselves a shot of winning that game. It speaks volumes for the group as a whole.
"It speaks volumes for the group as a whole. It is a fantastic group of men who care so much for playing for the All Blacks and making New Zealand proud. There is a lot of heartbreak in the sheds right now. It is hard."
Cane said that when he made his tackle on Springbok centre Jesse Kriel, he wasn't aware there was an issue.
"We have been here for two months now, and anything around the head has ramifications. I'm not here to discuss whether it was the right or wrong decision. It can't be changed.
"Unfortunately, it is something I am going to have to live with forever."