"It's being mentally hard on yourself and pushing yourself through that barrier when you know you're vulnerable and you're feeling good at the wicket. I've got out a few times in that period so if I can keep pushing myself through that period hopefully I will score a few hundreds.
"It was disappointing to get bowled out on the first day," the 25-year-old added. "We batted well in patches but a few loose shots and guys not applying themselves let us down. The guys are disappointed in the changing room at the moment. They know what they need to do for the next innings to rectify that - come out and score a few more runs."
Seamer Kemar Roach was the main beneficiary for the West Indies, picking up 4-70 after a good performance in his side's crushing victory in the first test.
Already missing the experienced Dan Vettori, with a groin strain, and opener Daniel Flynn with the same injury after his 45 and 20 in the first test, New Zealand were always going to be up against it.
Guptill and Taylor came together at 12-2 after the cheap dismissals of BJ Watling (2) and Brendon McCullum, who scored a four-ball duck, and both looked comfortable.
Taylor was quick to take advantage of anything loose - he hit 10 fours in his innings, which lasted 100 balls. Guptill was just as aggressive, hitting two massive sixes - he brought up New Zealand's 100 with one - as well as six fours.
After seeing the Black Caps through to 74-2 at lunch, Taylor picked up the pace but a Tino Best delivery cramped him and he was caught behind. Guptill was run out when attempting a quick single with Kruger van Wyk and succumbed to a direct throw from Best.