"We have not played a lot of test cricket so our performances haven't been as good as they should be," Vettori told reporters. "This team has the talent to succeed. We have to just get some performances under our belt."
The Kiwis arrived in Sri Lanka on Tuesday to play two test matches and a tri-nation limited-overs series against the hosts and India.
The 30-year-old Vettori is the most experienced player in the side with 92 test matches while 11 players in his 15-member test squad have only played 95 test matches between them.
Earlier this year, New Zealand played India in a three-match home test series which they lost 1-0.
Meanwhile, Sri Lanka is riding high after beating Pakistan 2-0 in last month's test series and has taken an unassailable 3-0 lead in their five-match limited-overs series with two matches still to be played.
"Our confidence grows with every win, we must take this into the next series ," Sri Lanka captain Kumar Sangakkara said.
The first test match between Sri Lanka and New Zealand will be played in Galle from August 18.
