The Boks won the second Test on the Castle Lager Outgoing Tour by 29-20 to make it two out of two on the tour with a match remaining, while the result also means South Africa will retain the No 1 spot on the world rankings.
“It was tough,” said Erasmus.
“We also had to work hard last week for the victory (against Scotland). We missed a kick here and there and both teams were disallowed tries in the second half, while the injury to Ox (Nche) disrupted the way we planned to do things.
“We were certainly not happy with the performance, but if you beat England by nine points, it could come across as arrogant to say that. So, we are content with the result.”
The Springboks scored four tries to two by England and kicked three conversions and a penalty goal to two penalty goals and two conversions by the hosts, who they last met in the Rugby World Cup semi-final.
The Boks are still on course to win all their matches on the traditional year-end tour, a feat they last achieved in 2013, with the trip concluding against Wales in Cardiff next Saturday.
The Boks held a narrow 19-17 lead going into halftime and managed to claw their way back from 20-19 down in the 51st minute to secure the nine-point victory despite playing with 14 men late in the match after replacement prop Gerhard Steenekamp received a yellow card.
However, the South Africans showed grit on defence and managed to deny the hosts a single point during that stage of the match to hold on for the victory.
Springbok captain Siya Kolisi lauded his charges for their fighting spirit: “We are a team that believe in fighting until the end and chasing lost causes, and that’s pulled us together as a group.
“We had to dig deep, but the players never gave up and kept on believing and that’s special about this group, and it allowed us to go all the way.”
With Erasmus making 12 changes to the starting team that faced Scotland, he admitted that while they felt pressure at certain points in the match, the team selected added some sense of comfort.
“We named an experienced team and one that has played important matches,” said the former Springbok loose forward.
“Many of them played in the closing match of the Castle Lager Rugby Championship against Argentina, but to hang in there with the yellow card, shows the planning the by the coaches.
“In fact, if Vincent (Koch) was not named as a loosehead prop on our team-sheet, we could have gone to uncontested scrums and had to play with 13 players on the field, so I’m pleased with the calm heads the players showed and how they remained calm and collected.”
Looking ahead at their final Test against Wales, Erasmus said: “Next week will be our last match and then we’ll see each other in June or July next year again, so we certainly want to end the tour on a high note.
“As coaches we first need to select the team and work really hard to analyse Wales properly and put our structures in place for the game, so that will be our focus next week.”
Erasmus said they would assess Nche’s injury in the next day or two after he suffered a cut above the knee which required stitches, and said they would determine his availability next week depending on his recovery.
The Springboks will travel from London to Cardiff on Sunday and will begin their on-field preparations for the match on Monday.