Ian Bell’s unbeaten century formed the backbone of England’s innings as they chased down a target of 227 with room to spare.
It was a positive end to a series they had already lost, and Cook was delighted with his players’ response in Dharamsala.
“It was a good win,” he said.
“It was important to win the toss, but the way our bowlers put the ball in the right areas and then Ian Bell’s contribution — we took our chances.
“We can take lots of positives out of today. The ball was doing stuff throughout the whole day.
“It might have looked like we got over the line comfortably but that wasn’t the case and there were a few nerves. But I knew if we held our nerve chasing 220 then we’d get there.
“It’s always disappointing to lose the series. But to win two games here in these conditions, we can be quite proud of that.”