"We've learned important lessons on how we should approach it in the future but our first priority is to get back in that situation."
Chasing an England-record 346 to win and resuming on 16-2,
the hosts attacked throughout the final day
and, when Matt Prior and Graeme Swann shared a rapid eighth-wicket stand of 78, an improbable victory looked increasingly likely.
But Swann was run out for 41 and Vernon Philander took two wickets in two balls to seal South Africa's victory in a
series they have dominated.
"When Prior and Swann were together I thought the chase was getting into the realms of possibility," Strauss, who was playing his 100th Test and 50th as captain, added. "If they'd put on another 20 or so then it would have looked like a fairly even contest.
"But South Africa definitely played the better cricket over the course of the three Test matches.
"We're bitterly disappointed but I can't fault the commitment, hunger and desire that everyone showed in this game.
"It was a fantastic effort but South Africa were just a bit too good. They have outplayed us in the course of this series and we have to find out why that is."
Prior, who kept England's hopes alive with a thrilling 73, was named as their man of the series.
"It almost hurts more when you get that close and to just fail to get over the line is very disappointing," the wicketkeeper said.
"We know that we have not lived up to our standards in the field and that is disappointing as it is something we pride ourselves on.
Test Match Special Analysis
Jonathan AgnewBBC cricket correspondent
"Now England have lost that number one spot, it is a chance for Andrew Strauss to look at his position. I am sure he will carry on for a while, but captains who lose series do tend to think about stepping down."
"The only thing now is to go away and put the time in off the field and try and get back to number one in the world."
The build-up to the final Test was dominated by the
controversy surrounding Kevin Pietersen,
who was dropped for sending text messages reportedly criticising Strauss to members of the South Africa team.
Strauss claimed the Pietersen issue did not affect England's performance and that talks to resolve the dispute will not take place in the near future.
The 35-year-old said: "It was a big thing in the build-up to the game but, in a tight, absorbing Test, it wasn't something that crossed our minds.
"I don't think anything will be happening straight away. The issues that need to be resolved will take a while and we'll be looking to do that away from the public eye."
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