South Africa captain Corne Krige apologised to his country's fans after his side's 25-6 defeat to England.
Juan Smith impressed for the Boks
The Springboks pushed the World Cup favourites all the way, with a charge-down try from Will Greenwood and 20 points from the boot of Jonny Wilkinson the difference between the sides.
"We knew we'd have to hit back quickly in the second-half," Krige said after both sides went into the break at 6-6.
"But we didn't manage it. We had good possession and they showed they are a world class side.
"It's very disappointing for us and we want to apologise to the people back home. We feel we've let them down."
England are now certain to top Pool C, with South Africa likely to book themselves a quarter-final clash against New Zealand.
"It is more difficult," Krige said. "But if you want to be world champions you have to beat every side."
Springbok coach Rudi Straeuli added: "At times we had them under pressure and there were two or three tries we didn't get.
"That's youth against experience. Against the top team in the world you've got to get those tries and kick those goals.
"It is obviously disappointing. We should have been up at half-time, and when
we stretched England out wide, I thought they were vulnerable."
Straeuli also insisted South Africa are far from out the World Cup, even if they have to play New Zealand in the quarter-finals.
"This tournament is not all over yet," he added. "Tonight showed that there is hope for South African rugby".