The pair made 145 for the fourth wicket before Pietersen (81) ran himself out after tea in an incident which very nearly soured England's day.
"KP (Pietersen) and Jonathan made it look easy, they played exceptionally well and the way they constructed their partnership was excellent, they each stuck to their own game plan," Strauss told a news conference.
"Those misunderstandings do happen in cricket, it's a shame, but I certainly won't be blaming anyone. I'd rather focus on their outstanding partnership in a pressure situation, they showed something special out there today," he said.
England, set 364 for victory, ended the first Test on 228 for nine with the last pair of Paul Collingwood and Graham Onions surviving for 3.1 overs after a dramatic collapse in which five wickets were lost for 13 runs.
"It was very important for us to get out of here with a draw, a loss would have hurt us badly. But we will be in good shape going into Durban, we're a confident group and nothing that's happened here will knock us," Strauss said.
The England captain put his team's collapse -- Ian Bell, Matt Prior, Stuart Broad and Graeme Swann scored just four runs between them -- down to the vagaries of the second new ball.
"It was a new-ball pitch and the new ball misbehaved throughout the test. You have to be phlegmatic about it, some of the batsmen got some pretty good balls," Strauss said.
Debutant fast bowler Friedel de Wet took three for 11 in seven overs in a top-class display with the second new ball, but South Africa captain Graeme Smith entrusted Makhaya Ntini, playing his 100th Test, with the final over.
"Friedel was on his knees and he had been for two overs. He was completely out of puff," Smith explained.
"It was frustrating not to win, but I'm not going to lose any sleep over it. I never thought England could win the test and we played the better cricket throughout.
"I don't care who has the balance of power going into Durban, because we can take a lot of confidence from the way we played," Smith said.
The second Test in Durban starts on December 26.
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