Young batsman Nair had scored an unbeaten 303 in India's innings and 75-run win against England in the fifth Test of the series.
Specifically asked about his expectations from David Warner, who has not made a hundred overseas since 2014, Smith said he must convert a century into a big one.
"It's pretty important that our senior players step up in those conditions and take control. It's something we didn't do overly well in Sri Lanka, and we didn't get the results that we wanted there. The senior players - myself, Davey, (Mitchell) Starcy, Josh (Hazlewood) and Nathan Lyon - need to step up and really take control," Smith told 'ESPNCricinfo'.
Smith said India is a difficult place to tour.
More From This Section
"India play incredibly well in their own backyard, and each individual is going to have to have plans in place. Ashwin and Jadeja have been incredible for a while now. They have got a couple of good quicks who bowl good reverse swing, and their batsmen score big runs," Smith said.
"Looking at the India-England series, England actually played reasonably well, they scored big runs, but India just went bigger and bigger. We are going to have to find ways to get them out and we are going to have to find ways to bat for long periods - 150 overs in your first innings and set the game up from there.
(REOPENS DEL 21)
Smith is not surprised with his team's spirited display in the series.
"We've worked very hard, guys have been pretty clear in the way they've wanted to play and the game plans they've been able to formulate. For me, the most pleasing thing is we have been able to take it out in the middle.
Smith said that the team has played to its potential against a quality side like India.
"India are a very tough side to play against, particularly here at home. We've seen the cricket they've played over this summer. They have played some very good cricket. For me, it was about us trying to find ways to play the way we need to play out here.