He told the post-match press conference that the All Blacks had deserved to win the game.
Discipline had been South Africa's biggest problem while the All Blacks had outscored them two tries to one.
A missed goal kick which rebounded off the posts from Handre Pollard might have been costly, he said, but it was all credit to New Zealand in the face of Sprinbok territorial advantage and scoreboard pressure they had taken their one opportunity to pounce to reverse the scoreboard pressure.
"We had to play a little bit more in our half and they started kicking little popper kicks to pin us back in our own half and we struggled to get out of there.
"That shows experience, that shows a world-class team and we struggled to handle that, so I think it is a combination of them putting pressure on us and us not handing that pressure very well," he said.
Erasmus said he felt South Africa could come back in the tournament, just as they had come back from being 3-17 down at halftime on Saturday.
It was ironic he said that the two times South Africa had tried to play some attacking rugby they had made mistakes which each led to All Blacks tries.
He recognised the achievements of rookie All Black wings George Bridge and Sevu Reece who, while inexperienced at Test level, had been 'unbelievable', and pounced really well when opportunities were available.
"New Zealand deserved to win, even if their tries were from turnovers they were just really good," he said.
Captain Siya Kolisi said the All Blacks had handled South Africa's kicking game very well.
"They were always ready for everything we threw at them and we didn't execute when we had the opportunities.
"eEvery time we were attacking we would make a mistake when we thought we were going forward and they would take the opportunity, they are very good off turnovers but all in all they really deserved today, they really played well. I can't fault them in any way," he said.
Erasmus said it had to be remembered South Africa were only ranked fifth in the world and teams like England, Ireland and Wales would provide the All Blacks with stiff competition going through to the finals.
"There's teams that can handle their kicking game and things they do and they might handle it a little better than we did on the day," he said.
The All Blacks and Springboks knew each other well from the number of times they had played recently but he believed the All Blacks were still the favourites for the World Cup.
Erasmus said people needed to remember that while the All Blacks attacked very well, they also had the ability to apply defensive pressure once they had scoreboard advantage.