Coach Ian Foster told SKY Sport that despite the loss the team had improved in key areas.
"We really did well at the lineout stuff, we defended their drives. Our defence, we weren't getting any calls, our defence was really strong. It was a game dominated by defence and dominated by a couple of high ball errors.
"I'm proud of the effort. They played a clinical game and we couldn't make the opportunities stick," he said.
Foster said they were frustrated at the way South Africa were throwing bodies in the air at catch contests for high balls, one of which saw Kurt-Lee Arense red-carded when taking out Beauden Barrett.
"That's something we've got to sort out. But if they're going to chuck bodies up, and just throw people at people in the air, it's a very hard thing to deal with.
"That's the game, we missed one and they scored and that got them early momentum.
"You could see how desperately we wanted it but their timing was just a fraction out against their line speed, and them coming in, particularly on our pivot side play.
"We've got to get better at that. We've got another chance next week. I think there was enough there to show we were moving in the right direction.
"It hurts to drop it, but these are always big Test matches over here and Ellis Park will be the same," he said.
Captain Sam Cane said, "In that first half we didn't really throw a punch. I thought we absorbed them pretty well, and we gave ourselves a good shot going into that second half.
"We couldn't get enough momentum going, largely due to Malcolm Marx over the pill.
"We were really up for this game, it is an honour to play the Springboks in their backyard and they were very good tonight. They played their brand of footy which can suffocate you if you are not good enough to take the high balls.
"I thought we defended the ball well but we didn't the high ball well enough and we didn't do a good enough job at the breakdown," he said.
"It's not like there's a lack of belief or effort or hard work trying to get us back on the right track but it's a very challenging time. We've got another week here so we've got to get back on the horse and start chipping away.
"We should stay positive and keep working because it's not far. It's not like we're a way off but it doesn't take away how disappointed we are with tonight because we really targeted this."
Springbok captain Siya Kolisi said they had been conscious of the danger New Zealand represented in broken play if they didn't get their kicks right. The Barrett brothers, Beauden and Jordie and Richie Mo'unga, who could create something out of nothing, so they had to be accurate with their kicking.
Knowing they were facing the All Blacks had created a different environment for the Springboks after their efforts against Wales in the July series.
"I know they are going to get better and next week will be tough because they do bring the best out of everyone," he said.
They had also shown the benefits of their fitness programme that started in 2018 because they knew they had to counter the All Blacks' ability to wear their big forwards out.