Off-spinner Ish Sodhi bowled 64 overs in the match, including 49 in the second innings, but he seems assured of playing at the Basin Reserve.
McCullum said the team would look to learn from the Test in Dunedin against England earlier this year where it bowled a lot of overs in the fourth innings and then produced a below-par effort in the second Test days later.
"The challenge for us is to replicate this. Last year against England, after a good Test match here we struggled in the second," he said, hinting that Doug Bracewell may get a start in Wellington.
Rival captain Darren Sammy was delighted when McCullum enforced the follow-on.
"Their bowlers toiled and that's a lot of yards in the legs. My bowlers will be much fresher than their bowlers," he said.
McCullum was adamant the decision to ask the West Indies to bat again was spot on.
"I think it was the right decision at the right time," he said.
Meanwhile, Sammy was hopeful his gluteal muscle injury would not rule him out of the next Test.
"I think with the combination of our squad it's important that I am able to bowl so I'll give it my best shot," he said.
Opening batsman Kraigg Brathwaite, called into the squad to cover for an injured Chris Gayle but whose arrival in New Zealand was delayed by visa issues, lands in Wellington on Monday.
New Zealand No.3 Kane Williamson, who missed the Test after failing to recover from a fractured thumb, appears likely to reclaim his place.
NZN