Buttler's 89 helped England recover from 198-7 on day one and score 332 runs in their first innings even as India struggled in bowler-friendly conditions.
"Yes, I think so (we are in-charge of the game)," Buttler said to a question after the end of second day here.
"The lead at the moment is quite healthy, and I hope if we can back up the performance today we can be in a really strong position in the game."
India still trail by 158 runs with 4 wickets remaining in their first innings.
Buttler had put on 33 runs with Adil Rashid and then 98 runs with Stuart Broad to bail out England.
Talking about his partnerships, Buttler said: "We probably spoke about 50 (more) runs that's what we were targeting. But I thought we worked really well in partnerships, and Rashid's got a lot of talent with the bat. And we know Broad's scored some vital runs for England over his career as well.
"What that does is give you confidence to stay in the same manner, and you don't have to change the way you're playing just because you're seven or eight down. We can just build a partnership as we did today," he added.
Indian skipper Virat Kohli again took the onus of scoring, as India struggled to 103-4 after being 70-1 at one stage.
James Anderson dismissed both Cheteshwar Pujara and Ajinkya Rahane but couldn't get Kohli, despite a massive lbw shout.
Kohli eventually was out for 49 to Ben Stokes towards the end of play as India slipped to 160-6 after losing Rishabh Pant as well.
"It's obviously a massive wicket. He's one of the best players in the world, and he's had an outstanding series. Any time you create a chance, or umpire's call early on can go either way, they are huge moments for us against a guy of that quality," said Buttler.
The 28-year-old batsman said it is a treat for the fans to watch the duel between Kohli and Anderson.
"It's fantastic Test cricket. Virat's one of the best players in the world, if not the best at the minute, and Jimmy's England's greatest ever bowler. As a match-up for fans and players alike, it's awesome to watch," he said.
"The two of them are immensely competitive and have a great duel all through the series."
Buttler said Anderson would have had more wickets if they could hold on to more catches.
"I think Jimmy has been particularly unlucky. He's created some great chances, and been very close. If we could catch, he'd have a few (wickets)," Buttler signed off.