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Having won the toss, New Zealand were rolled for just 45, their third lowest total, in 19.2 overs, effectively handing the test to South Africa.
Only Kane Williamson made double figures as New Zealand hit rock bottom.
''We had high hopes coming into today that we'd start well and it's extremely disappointing and there's a very hurt bunch of boys at the moment," he said.
''To have put in a performance like we did today you look around our changing room and we know we've let down our fans back home, which hurts a lot."
In response to the abysmal New Zealand effort, South Africa overcame the early loss of skipper Graeme Smith for 1, lbw to Doug Bracewell, to end the day on 252 for 3.
Smith's fellow opener Alviro Petersen was 103 not out, while Hashim Amla and Jacques Kallis made 66 and 60 respectively.
There was a wicket apiece for James Franklin and Trent Boult.
McCullum said New Zealand ''had to be better than that" after their stint at bat but heaped high praise on the remarkable Vernon Philander. He took the first five New Zealand wickets for just seven runs in a devastating performance of controlled seam bowling in only six overs.
New Zealand never recovered from that. Philander has now taken 26 wickets at 12 runs apiece in three and a-half tests against the Black Caps.
''That spell was as good a spell as you'd see in test cricket," McCullum said.
''He never misses his length and asks questions of you defensively in terms of defending your stumps but also managed to get the odd ball to kiss away.
''We weren't anywhere near where we need to be, all of us.
''None of us wanted it enough, or were able spend enough time at the crease to overcome the challenge laid down to us."
McCullum said he'd thought long about fielding first, but felt the pitch had dried significantly from the day before and had a few cracks. He knew it would be testing early ''but obviously not 10 for 45 challenging".
The task now for New Zealand was to salvage something from what remains of the match. South Africa will start the second day already 207 runs ahead with seven wickets standing.
''We've got to try and get the job done with the ball, get through the South African lineup and when we get the opportunity we've got to bat for our lives," McCullum said.
''We have to put in a performance which is worthy of the New Zealand cricket team."
Philander, playing in front of his home crowd, said there had been ''a little bit in the wicket, but I wouldn't say it was a 45 all out wicket".
''At Newlands there is always something in the morning, we obviously bowled well and got the ball in the right areas," he said.
Hearing he was fit after being in doubt with a hamstring strain had helped provide a spur for him to fire up.
''You need a bit of luck to go your way but obviously it went my way today."
His fellow quicks, Dale Steyn and Morne Morkel played their part, sharing the other five wickets.
In the case of the world's top-ranked bowler Steyn, he reached 300 test wickets with the first of his two wickets in the innings.
''He's a phenomenal bowler, he's No 1 for a reason," Philander said.
- David Leggat in Cape Town