The Kiwi captain gave due credit to Stuart Broad for his career-best bowling in a passage of play which saw the tourists - set 239 to win - collapse against the new ball to a terminal 29 for six before being bowled out for just 68 in 23 overs to go down 1-0 with one Test to play.
"It's pretty tough to explain," said McCullum. "For so long during this game, we were up with play, and at times I actually felt we were dictating terms. But in an hour, the game turned on its head, and I guess England continued to grow in confidence as they kept picking up wickets regularly."
He added: "Our confidence was starting to subside somewhat, and the difference between the two teams came down to that one hour of madness."
As Broad wreaked havoc in the middle, the Kiwis were at sixes and sevens in the pavilion too.
"Guys were getting their pads on and their pads off pretty quickly," added their captain. "You're looking for a calm presence somewhere - whether that's out in the middle or in the changing room.
"There was plenty of calmness about the guys in the changing room, and I just felt we weren't quite able to transfer that to the middle."
There was an unwelcome deja-vu for the tourists, who began this year by being bowled out for just 45 by South Africa's world-beating seam attack in Cape Town.
McCullum is hoping, however, that - having matched England, in three drawn Tests at home, and for so long here - they can rediscover their composure in time for the second and final match of the series in Leeds at the end of this week.
"We've had many of these experiences before. I think we've put distance between the last time that we felt this sort of pain and this time round, and I think we've taken some significant step forwards. But today was undoubtedly a step backwards inside that hour."
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