The Proteas managed to restrict England to 130-4 as the hosts attempted to chase down 253 having earlier restricted the tourists to 258-9 declared, thanks to a inspired spell by Stuart Broad (5-69).
“We felt it was worth having a go at it,” Strauss told Sky Sports.
“We sent in KP, who’s obviously in outstanding form, to set things in action but once Matt Prior got out it was probably time to shut up shop.
“It was a bit of a tall chase in the first place but it was certainly worth having a go.”
South Africa resumed on 39-0 overnight and were untroubled by England’s all-seam attack as Graeme Smith and Jacques Rudolph put on 120 for the first wicket.
It was in the unlikely form of Kevin Pietersen – who hinted that next week’s Test might be his final in an England shirt – that Strauss found the key to opening up South Africa’s innings.
The part-time off spinner removed the Proteas’ top three batsmen to finish with figures of 3-52.
Strauss will struggle to avoid criticism for dropping Graeme Swann, and regardless of Pietersen’s heroics, the game was still heading for an unsatisfactory draw.
Broad’s four wickets for 12 runs – including the wickets of AB de Villiers and JP Duminy in consecutive deliveries – gave England hope and set up the chance of a famous Headingley run chase.
South Africa had collapsed from 120 to 258-9 before Smith declared setting England 253 to win from just 39 overs.
The hosts showed real intent by opening the batting with Pietersen, but after the explosive right-hander was dismissed by Vernon Philander for a quick-fire 12 off 8 balls, any chance of an historic win was quashed.
England batted out to 130-4 before stumps, and now head to Lord’s for the final Test needing victory to level the series and remain number one in the world.
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