Skipper Darren Sammy is hoping West Indies can build on their 2-0 Test series win over New Zealand.
West Indies won the second Test in Jamaica by five wickets to complete their first series success over New Zealand for 16 years.
"We have gotten the feeling of what it is like to win, but we have to continue to work hard," said Sammy.
"The last year or two has been tough for us - we are going to celebrate this day, but it is about continuous hard work.
"The way Marlon (Samuels) held the innings together in both innings, that spell from Narsingh (Deonarine) yesterday, the performances are coming from different players at different times, that's the hallmark of a good team."
New Zealand captain Ross Taylor was disappointed by the 2-0 defeat, which rounded off a poor tour of the Caribbean.
"It's been a disappointing tour all round, we have had our chances in this match, in several matches this tour," he said afterwards.
"There are some positives, the bowlers bowled well on a tough wicket. We needed to set them 270-300 on what was a fourth-day wicket. We are a young team, we are getting better every now and then."