The game looked to be petering out into a draw when the hosts were set 259 for victory, but Strauss allowed Kevin Pietersen to open the batting before reverting back to defensive tactics after a flurry of wickets.
"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," Strauss told Sky Sports News. "It was a bit of a tall chase in the first place but it was certainly worth having a go.
"We just felt that if we let KP have a go, and then consolidate if he got out early, and then look at it a bit more and then try and get it into a Twenty20 situation towards the back end."
England have been dealt a blow by the news that Pietersen could retire from international cricket after the current Test series.