However, a grim, winless 2013 fast disappearing from the mind, they are certainly making significant strides after their 53-run win at Kensington Oval, Barbados.
"We're starting to play a brand of cricket people enjoy following and I think we're starting to win over the public as well which is important," McCullum said yesterday.
"We've just got to keep showing how good we can be. We were behind in this game for a long time but kept showing those fighting qualities we want to be known for.
"This series is certainly to be cherished for a long time."
McCullum and coach Mike Hesson will be aware that good teams don't sit on their hands for long. The next test assignment is against Pakistan in the United Arab Emirates.
The likelihood of at least one of the three opening batsmen in the Caribbean, Peter Fulton, making it are remote. Hamish Rutherford, too, has been shown up again.
The pair contributed 40 runs in six innings against the West Indies.
Elsewhere, however, the situation is rosy. Consider that at some point in the series, every other player used made an impact, although McCullum admitted his form wasn't flash. His leadership mattered though.
Kane Williamson, Tom Latham, Ross Taylor, the rapid riser Jimmy Neesham and wicketkeeper BJ Watling got important runs; Tim Southee, Trent Boult, Neil Wagner and spinners Mark Craig -- 12 wickets in his debut series -- and Ish Sodhi made decisive strikes in the series.
"You're always driven by the result and what you're trying to achieve," McCullum said. "We've got a great bunch of guys who are determined to perform for New Zealand and leave a legacy. At the moment things are good, but we've still got to improve."
He reserved special praise for man of the series Williamson, whose 413 runs included his sixth and seventh test hundreds.
Williamson is modest when talking about his own game. McCullum did his talking for him yesterday.
"He's the most selfless man, all about what the team needed and how he can perform a role for the team," he said.
McCullum said Williamson's unbeaten 161 in the second innings at Barbados, which laid the platform for the series clincher, was "sublime".
"His skill set is developing every day as is his mental application and game plan in general. He steps up in big situations. We're very lucky to have him."
It's worth remembering this West Indian team were distinctly stronger than the lame group who turned up in New Zealand late last year.
It is a series win to savour. Pakistan in November will be a distinctly different challenge.
However right now, New Zealand, home or away, look a team well up for any contest.
- By David Leggat of the NZ Herald
