South African captain Jean de Villiers felt his team took a step in the right direction, despite another loss against New Zealand.
He bemoaned his team's high error rate and poor discipline, but felt they still gave themselves a real chance of winning.
The All Blacks defeated South Africa 21-11 in their Rugby Championship encounter in Dunedin, which kept the hosts unbeaten after four matches - while the injury-hit Springboks saw their record slump to one win, a draw and two losses.
The All Blacks scored two tries, to Israel Dagg and Smith, while Aaron Cruden kicked three penalties and a conversion.
South Africa's points came from an exceptional try to Bryan Habana and penalties to Morné Steyn and Johann Goosen.
The win extended the All Blacks' unbeaten run to 14 games, three short of the world record 17 they share with the Boks.
In the first half the Springboks put away their kicking game and took the All Blacks on in the forwards with their confidence growing as they held their own in the bruising opening exchanges.
It kept the visitors within striking range of the posts but kickers Morné and Frans Steyn were woefully off target, being successful with only one of six shots at goal.
When the Springboks resorted to the boot early in the second half, a piece of individual brilliance by Habana produced an immediate try.
The right wing scoring machine charged straight through Cruden, then gathered in his own chip-kick over Richie McCaw's head to score in the corner.
It put South Africa ahead 8-3 with Morné Steyn again off target with the conversion attempt.
While the All Blacks were counting their blessings at the inaccuracy of the Springbok kickers, they were also ruing the Springboks' discipline.
It was not until the 51st minute that Cruden had his first penalty shot at goal and was successful from 30 metres to level the score at 8-8.
Replacement Aaron Smith then produced his magical try, which Cruden converted to put the All Blacks out to a 15-8 lead.
South Africa narrowed the gap to 15-11 when replacement flyhalf Goosen landed a penalty for his first international points, before Cruden kicked two more penalties for the All Blacks in the closing stages.
"I don't think many people gave us a chance," De Villiers said, when asked about his team's effort.
"We could have scored in the first couple of minutes, lost that opportunity, and again our goal-kicking wasn't great, so we definitely had the opportunities.
"At this level you can't make that many mistakes and not capitalise on your opportunities and think you will win the game ... a bit of the same every week.
"We need to improve, we need to get experience quickly and learn from our mistakes."
Asked about his team's persistence with the kicking game, De Villiers said: "We do get criticised that we kick too much.
"We feel that if we kick to get the ball back, not kick it away but regain the ball, that will be effective. At times we probably kicked possession away and that is definitely not what we want to do.
"It [the key] is getting that mix right."
However, he felt his team is making more progress than they are being given credit for.
"To put the best team in the world under pressure for 80 minutes and come so close and at the end could have won ... that is a step in the right direction."
He was pleased with his team's defence, but bemoaned the lack of discipline at times - with prop Dean Greyling yellow carded for foul play within minutes after coming on as a replacement.
"We played 10 minutes with only 14 men and probably our discipline at times wasn't great.
"We need to improve on that.
"As I said, you can't make that many mistakes against the best team in the world."