The 27-year-old Yorkshire batsman has been criticised by former players for his soft-spoken nature, with some suggesting he lacked the composure to lead under pressure.
But Root said the victory over India has given him confidence that his long-term plans for the team were taking shape.
"I feel like I've had quite a big input into what has been going on, felt in control of things and I've got a real clear vision of how I see us improving long-term," Root added.
"We've got some guys who are very willing to buy into that, and are very realistic and understanding of where we currently are and where we could really get to.
Asked if it was his best victory since taking over as captain last February, Root told reporters: "Yes, I think it probably has been."
"I hope it's a big step in the right direction and we can go from strength to strength. When you have that understanding across the board and there's no selfish people within a team, it makes it very easy."
The final test of the series starts at The Oval on Friday.
(Reporting by Shrivathsa Sridhar in Bengaluru)
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