Virat has been rested for the first Test and Ajinkya Rahane will lead the side in his absence, while the regular captain will return for the second Test in Mumbai beginning December 3.
Smith, 60, who has played 63 Tests for the Black Caps scoring more than 1800 runs, is also unhappy with Rohit Sharma being rested for the two-Test series.
"India have left out Kohli and Sharma, it intrigues me actually that we're resting people in Test cricket these days, that disappoints me greatly," Smith told sen.com.au on Tuesday.
Smith said that New Zealand should play three spinners in the Kanpur Test, given the nature of the sub-continental pitches. He also named the eleven players he would like to see skipper Kane Williamson field in the opening Test.
"You've got to have (Neil) Wagner so when you get in trouble, he can try and bowl you out of it with his stamina," said Smith, indicating that he wants the fiery pace bowler to bowl longer spells to unsettle the Indians.
Smith's XI for New Zealand Tom Latham, Will Young, Kane Williamson, Ross Taylor, Henry Nicholls, Tom Blundell, Rachin Ravindra, William Somerville, Ajaz Patel, Kyle Jamieson, Neil Wagner.
Auckland, Nov 23
Former New Zealand wicketkeeper-batter Ian Smith is not happy with the Board of Control for Cricket in India's (BCCI) decision to rest Test skipper Virat Kohli for the opening game against the Kane Williamson-led side, beginning in Kanpur on November 25.
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