Visitors had set a target of 420 runs in Chennai
England beat India by 227 runs in the first Test after bowling out the home side for 192 in Chennai on Tuesday.
Spinner Jack Leach claimed four wickets and paceman James Anderson three as England ended India's hopes of chasing a record 420 to win in the afternoon session of the final day.
Skipper Joe Root scored 218 to guide England to 578 in the first innings and 40 in their second innings of 179. India hit 337 in their first innings.
Root, England captain and player of the match in his 100th Test, praised his side for dominating the Test match.
“Yeah, from the toss [things seemed to go our way]. It was a crucial toss and we posted a very good score and to score 20 wickets in alien conditions...huge credit to the bowlers. The first partnership was crucial to get us going and from there it was about contributions. That's got to be the way we have to win out there - bat for long periods for time in the first innings,” said Root after the match.
“We are a proud team and it's important to keep finding ways to get better. The idea was to get to 400 and declare and it didn't materialise like that. The most important thing was to take the Indian win out of the equation and we could just focus on taking the wickets. I think the guys handled the pressure well and looking forward to the rest of the series,” he added.
Root also spoke highly of veteran pacer James Anderson for playing a key role in the team’s victory.
“The way he (Anderson) goes about things - constantly challenging himself at 38 to still get better - he's a great role model to the rest of the ground. And his skill level is right up there,” he said.
Meanwhile, losing captain Kohli admitted that England played better cricket over the course of the match but backed his team to comeback in the upcoming matches.
“England played far more professionally. You need your bowling unit to step up and perform more collectively. It’s okay, lack of execution is understandable. We're always learning as a side. Test cricket is a grind. England were ready for the grind and were far more equipped,” said Kohli.
“Firstly start off with good body language, understand the fields, and at the end of the day it's the mindset. As a side, we're a side that always improves and knows how to bounce back,” he added.