The Proteas' 51-run win at Lord's allowed them to take the three-match series 2-0 and with it, whip the No.1 ranking from under their hosts' feet.
Short of a thrilling late rally led by Matt Prior (73), South Africa, with their superior batting, always looked in complete control.
"This was an outstanding Test and there was some good, first-class cricket on show," said the England captain.
"We were never the favourites today but the guys showed spirit and the attitude they showed was of great credit to the players.
"South Africa were the better side over the course of the series and thoroughly deserved their victory."
Chasing what would have been a record 346 to win, Strauss' men occasionally flirted with pulling off a great escape act with Prior, Jonathan Trott (63), Jonny Bairstow (54) and Graeme Swann (41) all swinging the bat to great effect.
The accuracy of Vernon Philander (five for 30) tore them apart, though, and left Strauss planning a route back to the summit.
"You can't fault the commitment, we gave it everything and this was how I expected it to pan out," he said. "Small, tight margins. They were just better than us. I don't look back on our time as No.1 with a great deal of fondness, as we had some tough times. That can be a good thing, though, as Test cricket tests you when you're No.1. We've learned a lot and it's a shame to hand it over, but they deserve to be No.1 and we will come back."
Strauss' opposite number Graeme Smith dedicated the win to former wicket-keeper Mark Boucher who was forced into international retirement on the eve of the series when he suffered a serious eye injury in a warm-up match.
He was watching on television, though, and Smith, wearing a shirt which read "we miss you Bouch" said: "This is a message from all of us. He's been part of us for 147 games and this was meant to be his 150th. This victory was for him and for everything he has done for us." Of the game, Smith added: "It was a top Test, both teams played well, England played with freedom and we had to work hard. There was some great batting from Swann and Prior but it was wonderful to come through."
Prior was named England's man of the series, not just for his knock yesterday but for consistent contributions throughout the summer.
"It almost hurts more to get that close and lose," said the man who almost led England to a memorable victory. "It's very disappointing. You never think it's over as the wicket usually stays good for the five days at Lord's. But congratulations to South Africa, they were brilliant all series."