He told SKY Sport: "It's never a question of how much we care, or how much we want it, but we seemed to get a few parts of our game right.
'It was a massive challenge coming here, one of the toughest places in the world to play and the group stepped up massively."
Cane thanked those who supported the side over the last month because the team had felt that support.
"We were a lot better at the breakdown tonight and we dealt with the box kicks, and contestables, a lot better.
"The set-piece was good, we defended the maul really well, so it was lots of little parts of our game right, which is what Test footy is about, getting little parts of your game right time and time again, so you can build some pressure."
Coach Ian Foster said there was no doubt it was a special time for a team that had been trying to find their feet.
"We've worked hard, it's never easy when you're coming off a couple of losses, but I'm so proud of the effort. It's swings and roundabouts and we hung in there and finished strong."
Foster said the shift he acknowledged the forward pack made in the first Test at Mbombela last week was reflected at Ellis Park on Saturday.
The work put in by new forwards coach Jason Ryan kicked in and they eliminated the rushing mistakes and were more patient.
"When you start believing in yourself, you get more patient, and then you start to execute. And that's what it looked like tonight," he said.
It had been two bad moments in the All Blacks' game, from restarts, that kept South Africa in the game, he said.
Foster felt new props Ethan de Groot and Tyrell Lomax had scrummed well, hooker Samisoni Taukei'aho continued to grow while debut player Fletcher Newell had been good off the bench.
First five-eighths Richie Mo'unga played well and brought belief to what the side wanted to achieve, he said.
"There was some good positive things, and there's more to come," Foster said.
Mo'unga said the win was hard to put into words.
"To put something out there we could be proud of, and something that we knew we were capable of, is awesome, I'm really proud."
He said he was hungry to start the Test and he knew how much influence he could bring to the effort.
Mo'unga said he saw what the side was capable of two weeks ago, not just after this win.
"For every successful team there has always been a part where there is adversity, there's been ups and downs, things that have changed the team. I think this is it for us putting a lot of pressure on the Springboks team, and what a world-class team they are," he said.
"We knew we were close. We've said it the last couple of weeks and, as I said during the week, close isn't good enough.
"But we were one pass away, one tackle away, in turning things around and I think we've done something pretty special here tonight.
"But the challenge is going back-to-back. It's about doing this [in our] next performance and keeping the standards really high.
"We want to build on this, use this momentum, keep turning up being better. I know it's really cliché, but those little things will make the difference and turn this team into a world-class team."