Stuart Lancaster's men now head into next weekend's appointment with world champions New Zealand on the back of narrow defeats at home to Australia and the Springboks.
England competed every step of the way with South Africa, matching the Springboks for intensity and desire and they battled back from 16-6 down with real heart.
They were the better team, particularly in the second half when Owen Farrell came on, but their undoing was a slice of bad luck just after the interval.
When Ben Youngs' hacked clearance rebounded off JP Pietersen, the ball fell to Alberts who scored rugby's equivalent of an open goal.
Farrell added three penalties to the two struck by Toby Flood as England battled all the way to the death. Lancaster will be encouraged by those qualities.
But assistant coach Graham Rowntree himself said yesterday that he was sick of talking about lessons learned and England, despite Alberts' fortunate try, could have won the game.
Flood missed two first-half penalties and again the spotlight will fall on a decision made by captain Chris Robshaw when England were awarded a kickable penalty with just over a minute remaining.
Last week, England were criticised for not taking their points. Today, Robshaw changed his mind having initially told Farrell to kick for touch.
Farrell slotted the penalty, but England could not gather the restart and South Africa held on to extend their unbeaten run in this fixture to 11 matches, dating back to 2006.
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