The Springboks were hoping to end an 88-year wait for a Test match win at the venue, where New Zealand have not lost to anyone since France beat them in 1994.
But the visitors' error count, both on defence and attack, was too high.
"We were 14 points behind after two easy tries, and we found ourselves chasing our own tails, and that was in the rain as well," Erasmus told reporters.
"I thought the replacements brought energy, and we fought back well, but it’s tough to win if you are 14 points behind.
"We made two individual errors and they scored tries, and the other times they had to grind, so it’s frustrating.
"It’s not always the same players making the mistakes, and some of them were stupid errors. But as coaches, we pick the players, and as management, we have to sometimes put up our hands and say we got it wrong."
Much was made of the history between the sides at Eden Park, where the Springboks last won in 1937. They will face New Zealand in a second Rugby Championship clash in Wellington next Saturday.
"If we had won, we would probably have mentioned the history, but they managed to maintain their record at Eden Park, and well done to them for that," said Erasmus.
"It was a great challenge for us, but we didn’t achieve it. That said, we have another chance to face them next week."
South Africa will likely have to win their second clash with New Zealand to keep alive their hopes of retaining their Rugby Championship title.
"The one positive is that we are still in the race for the Rugby Championship title, and if one looks at the match, we played badly for 15 minutes and as the game progressed, we got better," he said.
"We are very disappointed, but we played the number one team in the world, and we have to put everything into trying to win next week."