Clueless shotmaking and sloppy decision-making undid New Zealand, who had begun their second innings 91 runs adrift but in supposedly the best batting conditions of the test.
It is galling to think that South Africa's No 11 Morne Morkel made 40 in one innings; Tom Latham, Williamson and Neil Broom, all in the top four, made a combined 37 in six innings.
New Zealand need to think back to Dunedin and the good parts of the Basin test as they prepare for Seddon Park.
"Yesterday (Saturday) was a terrible day. To lose within three days is unacceptable," McMillan said. "But it's important to remember just over a week ago we performed pretty well in the first test, and make sure we bounce back quickly in Hamilton."
The complete failure to cope with Maharaj - now owner of the best figures by an overseas spinner at the Basin - was a surprise.
"We didn't assess that over the three days the pitch wasn't turning. We had a couple of stumpings where guys were expecting it to turn and it didn't. We just have to be smarter with that," McMillan said.
Asked after the test why he hadn't used New Zealand's only spinner, Jeetan Patel, at all after Maharaj's destructive couple of hours, albeit defending only 81, Williamson was momentarily lost for words.
"I didn't think it was spinning a huge amount," he finally said, clearly still coming to terms with what he'd seen and still not really believing it.
The Seddon Park pitch has produced three successive test wins for New Zealand, versus West Indies, Sri Lanka and, in November, Pakistan. It has been a good test venue, 10 wins out of 22 tests.
But McMillan was unsure what to expect.
He believes the pitch is on the Waikari clay half of the block, which suggests slower pace and a greater propensity to spin. But he remains confident New Zealand can perform whatever conditions they are presented with.
Swing man Trent Boult (upper leg injury) and senior batsman Ross Taylor (minor calf tear) will join the group in the hope they'll be ready to return. Boult is a good chance; Taylor iffy.
"It's up to us to assess and adapt to the conditions," he said.
Being one down with one to play won't change the way New Zealand aim to go about their business, McMillan added.
"You've got to get that platform and whatever you are doing just be nice and consistent, and when those pressure points come up you've got to have someone stand up and grab them."
Unfortunately that's what they had at the Basin, and wasted it.