"I think so, I think there's an area there," Wright said when asked if New Zealand Cricket should seek an extra employee.
"I can talk to say, Tarun, and talk to him about a few technique things, but it's always based around medium fast-bowling and the approach that I have towards that.
"There are areas in the spin bowling where he needs to listen to a specialist spin bowling coach."
Wright, who for family reasons is reluctantly stepping aside, thought that coach was even more essential in New Zealand where spin bowling isn't in the blood as it is in this part of the world.
"Especially in countries like New Zealand and Australia where our spin bowlers aren't as effective as the sub-continent bowlers," he said. "It'd be nice for them. If you talk to them I'm sure they'd like to have a specialist coach."
An extra coach may not have helped New Zealand to fully close the gap to the hosts last week but, after toying with the idea, perhaps Nethula could have played in partnership with Patel had he been aided by the assistance of a spinner by trade.
And that would have provided a different dimension to their attack because, as India showed, two tweakers are almost as crucial on the sub-continent as a fondness for curry.
The duel spin attack may be employed for the second test, starting on Friday in Bangalore, but that would also rob New Zealand of another member of their five-strong seam bowling stocks. Already Tim Southee and Neil Wagner have had to sit on the sidelines on this tour and ushering in that depth was one thing Wright was most pleased with in his tenure.
"I hope that I've had an influence over the younger guys, in particular Doug Bracewell and Trent Boult and Tim Southee," Wright said. "Hopefully I've showed them a thing or two."
Since taking over from Alan Donald last year, Wright has relished guiding the emergence of the likes of Bracewell and Boult, and the coach was loathe to leave the set-up now, but family came first.
"It was certainly very hard for me to come around on," he said. "I'm really keen to stay on and I'm thoroughly enjoying the role but, unfortunately, it's just a little bit hard on the home front at the moment.
"With a long time away from home and things like that, it's been really tough."