The tourists were bowled out for 167 in their first innings, but managed to hold on for a draw earlier today.
The captain told BBC Sport: "It is a concern. I'm not quite sure we know the reason for it. I thought we did well to claw it back but we've been lucky certainly, in one sense, to escape with a draw.
"You can give credit to New Zealand and the way they bowled and put us under pressure, but the bottom line is we played a lot of soft shots and gifted them our wickets.
"In the bigger picture we need to start better than that. It's a huge reminder that, if you don't perform, you don't deserve to win anything, but the character we showed to dig ourselves out of that hole is very pleasing."
The two nations meet again in Wellington for the second Test from Wednesday evening.