They combined to skittle New Zealand for just 45 in the first 100 minutes of the match, then shared a further six wickets in the second innings of 275, which set up an innings and 27-run win.
"It's up there, that's for sure," McCullum said when asked if they were the best he'd come across.
"Australia's attack of a few years ago [headed by Glenn McGrath, Jason Gillespie and Brett Lee] was pretty relentless. But the South Africans keep coming hard at you and constantly put you under pressure. Their seam attack is right up there and certainly No 1 attack in the world."
Steyn took his 300th wicket in the match, and 50th against New Zealand in his ninth test.
He took five wickets in the match, Morne Morkel four-and-man-of-the-match Vernon Philander finished with seven for 83 in the game.
McCullum understandably felt New Zealand had made a far better fist of handling those three bowlers in the second innings. His team's job now is to pick the good bits out of an awful test, and turn them into elements which they can turn to their advantage leading up to the second and final test, which starts at Port Elizabeth on Friday.
South African captain Graeme Smith praised the resilience within his squad.
"The biggest thing is the understanding of what needs to be done, then going and doing it," he said. "We've worked our backsides off to get back into games and when we had that opportunity we've really driven a bus through the door."
He had expected New Zealand to put up a far more resolute effort in their second innings than the first, to "really guts it out".
"They showed good discipline. They were fairly defensive in their mindset but I thought we bowled really well."
McCullum was left to rue the failure of New Zealand to push the game into at least a fourth day at one of the finest grounds in world cricket.
"We don't tend to get to play in front of packed houses, but it was a real treat. It was amazing, especially with quite a young group. It's a special ground and it would have been nice to have had days four and five in front of a weekend crowd."
South Africa have rewarded their players by sending them home for an unexpected three days off.
New Zealand head to Port Elilzabeth on Tuesday, after a period of hard thinking about what had just happened, and what lies ahead.
- By David Leggat of the New Zealand Herald in Cape Town
