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 as 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 at least be encouraged by those qualities.
England captain Chris Robshaw said: "I thought we could take the three points, get down field for a drop goal. But unfortunately it was not to be."
Ireland scored seven tries in a 46-24 demolition of Argentina to ensure they will be seeded when the draw is made for the next World Cup and leave the South Americans waiting to find out if they will join them.
Ireland had to win the match, billed as the most important one either side would likely play this side of the 2015 tournament, to book a place in the second tier of seeds for the December 3 draw, and four tries in a blistering first half got them on their way. Debutant wing Craig Gilroy got his first try, as did Simon Zebo and Richardt Strauss, while Jonathan Sexton and Tommy Bowe got a brace each to maintain Ireland's unbeaten home record against Argentina.
In Florence, Australia survived a second-half fightback to maintain their perfect record against Italy, winning 22-19.
The Wallabies had looked to be coasting after Nick Cummins' second try in as many weeks helped them into a 22-3 half-time lead. But Robbie Deans' men ground to a halt as the Azzurri pushed for their first win over Australia.