The 27-year-old Kohli, leading in his second home series and first under new head coach Anil Kumble, said "patience" and the value of the lower order contributing with the bat were big factors in India's 197-run win against New Zealand.
On raging turners, where many matches have finished inside four days, India have won each of their last three home series, against Australia, the West Indies and South Africa, without losing a Test. The Kiwis did well to take the Green Park Test to the fifth day.
Kohli credited the Kiwis for "showing character" and the resilience against India's spinners who took 16 New Zealand wickets. Ravichandran Ashwin had an outstanding match with a 10-wicket haul.
Mitchell Santner's 71 off 179 balls in the second innings underlined New Zealand's fighting spirit and Kohli said it was important to be patient when wickets were not falling.
"I am still pretty early in my captaincy career. We have to patient when wickets don't fall. The important thing is to not to leak extra runs," Kohli said in his post-match chat.
India's ability to bat deep has been a focus area for the team, Kohli said.
"Most important thing is a strong lower-middle order. We are working hard with the bowlers. Down Ashwin, Wriddhiman Saha, Ravindra Jadeja want to contribute. (Amit) Mishra has done in the past. Forty-50-60 runs are crucial," Kohli said.
Kohli is expecting a good fight from the Kiwis in second Test in Kolkata starting September 30.