"Most definitely," the lion-hearted competitor from Barbados said.
"We have the batting talent in our team to bat long periods. We need to put our hands up and be counted."
Taking a leaf from New Zealand's batsmen would help, he added.
"Occupation of the crease is very important, and shot selection. New Zealand leave a lot alone. We have to adopt the same attitude."
Wagner talked of a dressing room "fizzing". "One thing about the West Indies is they like to be positive.
"If we do our disciplines well and consistently we'll definitely give ourselves a chance."
Wagner talked of the importance of the first hour today. Get early wickets, put the squeeze on and they would have forced open the door, he said.
Trent Boult and Tim Southee turned the handle and inched it open late yesterday, removing openers Kirk Edwards and Kieran Powell to catches behind the wicket.
Darren Bravo and Marlon Samuels are at the crease and look a cut above the openers and the barnacle, Shiv Chanderpaulin his 151st test, is next in.
New Zealand made their highest total since Napier in 2009 against India, 619 for nine.
Now it's the bowlers' turn to deliver. Legspinner Ish Sodhi caught the eye late on with turn and bounce, and would have had Bravo caught with his second ball had there been a silly mid-off.
The day began with Brendon McCullum and Taylor walking out as the first pair of New Zealand batsmen to start a day with a century apiece.
Taylor found solid support from BJ Watling (84 for the sixth wicket), Sodhi (76 for the eighth) and Wagner (61 for the ninth).
The West Indies were hampered by captain and third seamer Darren Sammy being unable to bowl from midway through the first session with a gluteal strain.
Their fielding was again ordinary, as was much of the bowling, Best the diligent exception.
"My mother told me there'd be days like this," the outgoing Best muttered.
The West Indies batsmen have to be far more impressive if his confidence in his teammates is to be repaid.
Making their mark
* New Zealand's 609 for nine declared is its fourth highest test total, behind 671-4 (v Sri Lanka, Wellington, 1991), 630-6 (v India, Mohali, 2003) and 619-9 dec (v India, Napier, 2009).
* It is the highest total made by New Zealand after being sent in to bat, eclipsing the 593-8 v South Africa at Cape Town in 2006.
* The total beat the old mark against the West Indies of 543-3 at Guyana in 1972.