''We're going to have to raise our game again, which is exciting because you want to be pushing the envelope of how good you can be and that's what we're going to have to do."
Sri Lanka were dismissed for 282 soon after lunch yesterday, after being set 405 to win.
They could have got far closer to what would have been the fourth highest successful chase in test history too, had it not been for a couple of piece of calamitous judgement before lunch from their best batsmen.
Consider the pitch was still playing well and both Mathews and Dinesh Chandimal were set.
So Mathews' decision to aim a boot away a ball from Neil Wagner to the onside, which cannoned back onto his middle stump was bizarre.
Chandimal, on 58 and completing a fine double in the test, played no shot to offspinner Mitchell Santner.
These days, with the DRS system, batsmen cannot apply the same impunity to defensive batting that they did in the pre-technology days.
Still, New Zealand bossed this test from the first session, when they got to 114 for one, having been sent in, and didn't relinquish their grip.
The batting group did their job expertly, laying the groundwork with 400-plus runs on day one; pressed home the initiative in the second innings; and stuck to their bowling task in testing conditions in both Sri Lankan innings.
The DRS had its say yesterday too with five decisions required in the morning session.
But while McCullum was reluctant to talk much about it, citing a lack of real specialist knowledge about its inner workings, he wanted the attention to be on the on-field performance.
''I'd hope the focus will be on how hard we had to work for the 20 wickets and how well we played throughout the test match rather than focusing too much on the DRS," he said.
It was appropriate Doug Bracewell took the final wicket, a caught and bowled, as it was his only wicket in the test. He bowled far better than that suggests.
Mathews had no quibble with the target set, knowing that with a good start ''we could have given it a go".
''The run rate wasn't a massive worry for us. It's just the wickets. We had to have wickets in hand."
Tim Southee led the New Zealand attack strongly, and was rewarded with six wickets.
Trent Boult looked down on pace while Santner picked up four wickets, varying from the tight-fisted to the loose.
The idea for New Zealand, having delivered the first blows in the series, is now to stay on top.
-By David Leggat in Dunedin
SCOREBOARD
WAGONWHEEL
MANHATTAN