Sam Cane admitted that the heartbreak of his costly red card in his side’s one-point World Cup final defeat by South Africa was something “I’m going to have to live with for ever”.

The New Zealand captain was sent off via the bunker review system for a high tackle on Jesse Kriel just before the half-hour mark of South Africa’s 12-11 victory. South Africa led 9-3 at the time and extended their lead to nine points but the 14-man All Blacks rallied after the break and scored the only try of the match through Beauden Barrett, but came up agonisingly short.

Related: South Africa beat New Zealand to win men’s Rugby World Cup final

The upshot is that South Africa are the first team to ever win the World Cup on four occasions and become only the second team – after New Zealand in 2015 – to successfully defend their title. The Springboks edged home thanks to four penalties from Handré Pollard, winning their third consecutive knockout match by a single point.

“So much hurt right now,” said Cane. “It’s hard to find the words to explain it. It’s hard because I’m feeling so much hurt but proud because of the way we fought back. It speaks volumes of the group as a whole. A fantastic group of men who care so much about the ABs. There’s a lot of heartbreak in the shed and it’s hard. It’s something unfortunately I’m going to have to live with for ever.”

South Africa’s captain, Siya Kolisi, was shown a yellow card in the 45th minute for a high tackle on Ardie Savea but that was not upgraded, leaving the outgoing All Blacks coach, Ian Foster, unimpressed at the inconsistency. “I really don’t want the game to be about us talking about red cards,” said Foster. “It is what it is. There will be plenty of time to analyse that. There was an intent to wrap [by Cane], there didn’t seem to be a whole lot of force in the contact. The hit on Ardie had a lot of force going into that contact and had a direct contact on the head. The game has got a few issues it has got to sort out. That’s not sour grapes. You’ve got two different situations with different variables and one is a red card, one is a yellow card. That is the game.”

Related: South Africa prove to be masters of finding point of difference

Kolisi – one of 10 players to start this final and the 2019 triumph over England – paid tribute to the people of South Africa after their nail-biting victory. “We were kind of just hoping to win in the last World Cup, but this time people were expecting it,” said Kolisi. “There is so much going wrong in our country, and we are like the last line of defence and we can show that we can achieve so much together. There were people before me who fought for people who look like me to even be able to play for this team, so it’s my duty to make sure we make this team all it can be and inspire more people.

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“People who are not from South Africa don’t understand what it means for our country. It is not just about the game. Our country goes through such a lot. We are just grateful that we can be here. I want to tell the people of South Africa: ‘Thank you so much.’”