With the win in the Mumbai Test, the Kohli-led team secured the five-match series against England and the emphatic performance came after India got the better of New Zealand, West Indies, South Africa and Sri Lanka in the previous rubbers.
Asked about the air of invincibility surrounding the team ahead of the fifth Test starting tomorrow, Kohli replied in the negative.
"It (the phase) looks really good because we have come out of transition and immediately started winning games. But I wouldn't take this as overconfidence.
"As I said, it's an ongoing process which needs to be sustained for the next five-seven or eight years for us to become a top quality side and leave a mark on world cricket; maybe known as one of the best teams to have assembled on the field."
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"We want to do it across formats and make that mark for Indian cricket on the world stage. But it requires a lot of persistence and skill, lot of hard work on your fitness and those are the key factors which will decide where we go as a unit.
"We don't feel invincible to be honest, we respect every opposition, we admit every time we are put under pressure, and we know teams are going to put us under pressure. We appreciate that, we accept that and we try to find a way out of it.
Talking about the dead rubber beginning tomorrow, Kohli said the match remains an important one for the hosts.
"I don't think we are looking at a collective series as 4-0. For us every game is separate from the other and the intensity and the motivation to win a Test match remains the same, whether we have won the series or haven't won the series, or it's drawn.
The Indian spinners led by Ravichandran Ashwin have not just delivered with the ball but have also made valuable contributions with the bat, allowing Kohli to play five specialist batsmen and as many bowlers.
In the media interaction, Kohli again showered praise on Ashwin, Ravindra Jadeja and rookie Jayant Yadav, who scored a hundred in Mumbai batting at number nine.
"Their contributions with the bat have been outstanding. Hasn't taken much from me at all to motivate them. I think Ashwin has set a benchmark for the other spinners to contribute with the bat as well.
"Jadeja has come of age with the bat in this series, we saw his knock in Mohali, where he went out with lot of confidence and scored 90 runs for us. Jayant Yadav as well. He gets inspired seeing Ashwin the way he improves his cricket every time. Jayant always has been a keen learner.
"So as a captain it gives you more freedom to play five batsmen rather than thinking of another batsman when your bowlers contribute 120-130 runs in every game for you," said Kohli.
Kohli said Jayant's approach reminded him of the great England spinner Graeme Swann.
"Jayant, what he has done, he has come in and has his plans. Has a lot of control as well and he rushes the batsman. If you saw the way he got his wickets in Vizag he rushed Stokes, in Mohali he rushed Root where he got LBW.
"The pace control was magnificent without giving the ball too much air and that's why he was so successful. That's what I see with Jayant as well.
"So as a captain I know that the third bowler is one against whom the batsmen cannot independently go after and that brings him into the game at any stage whenever you want a wicket, Jayant is always there on the spot, making things happen and creating doubt in the batsman's head," said the star batsman who himself has been in top form in the series amassing 640 runs in four games.