India were in a strong position at 154 for 1 at one stage before a middle-order collapse saw them reduce to 291 for 9 at stumps on the opening day.
Vijay top-scored for the hosts with a 65 but himself played a poor shot, a cut off a not-so-short ball off leg-break bowler Ish Sodhi and was caught behind.
Asked if it was lack of application from the batsmen or the wicket that resulted to India losing the advantage, Vijay said, it was a "bit of both".
"We got out to loose shots as well and wicket was deteriorating as well, so we really got to be patient on this wicket. It's a lesson learnt and hopefully we can put up a better show in the second innings," Vijay said at the press conference.
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Talking about his own shot, Vijay said it was out of lapse of concentration.
The Tamil Nadu opener said that despite losing wickets in a heap, India were in a "good position".
"We have put runs on the board. What we have got to do now is go there and put pressure on them. It's a good total to play around with," he said with confidence.
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Asked how the team felt in the dressing room when Rohit, who had stabilised the innings with his 52-run partnership with Ravichandran Ashwin, got out by chipping the ball to Sodhi, Vijay said, "That's his area, when it comes out good, it looks good. When it does not, you fall on the wrong side. We still got to back our instincts.
Vijay said the New Zealand spin attack was decent.
"I would say, they had a good attack. According to situation, we got to make a play out of it. We knew this is going to be the plan (Kiwis fielding three spinners), we were well prepared for it. We could have capitalized a bit more after tea," he said.
Vijay had a single digit score (of 7) to show in India's previous assignment in the West Indies as he came in and out of the team.