Captain Joe Root said it is important England do not get "complacent" or "arrogant" as they pursue their "dream" of a 5-0 series win over India.
England took a 2-0 series lead by thrashing India by an innings and 159 runs in the second Test at Lord's.
The win came in just 170.3 overs against the world's top-ranked side.
"We've set it up nicely to be 2-0 up, but there are three big games against a good side and we're going to have to play well," Root said.
"Obviously, that would be the dream - to put in five complete performances and have five wins.
"But it's important we don't get complacent, arrogant, or look too far ahead.
"We're not the finished article - we've got a long way to go to where we want to get to."
'We've got to enjoy Anderson while he's around'
Bowler James Anderson starred in the match taking 9-43 and claiming his 100th wicket at Lord's, becoming just the second bowler to take 100 wickets at a single ground, after Sri Lanka's Muttiah Muralitharan.
The 36-year-old also took his career total to 553 Test wickets, 10 behind Australian Glenn McGrath, who holds the record for a quick bowler.
"He's something that doesn't come along very often and we've got to enjoy him while he's around," Root said.
"There's been chat about his longevity but at the minute he's bowling better than he ever has before.
"For him to be performing as he is, is something else.
"It's great to watch, and to be a part of. He's a massive part of this team."
Root not concerned about top order
The victory for England came despite another poor performance from their top order.
Openers Alastair Cook (21) and Keaton Jennings (11) were both dismissed cheaply after disappointing first Tests while Ollie Pope, making his Test debut in place of the dropped Dawid Malan, scored 28.
However, Root said the form of his top five batsman was "not a worry".
"It's being quite realistic with what's happened within the game, not looking at the numbers," he said.
"I'm quite happy with the side, the players we've got.
"You've got to be quite realistic with the surfaces we've played on, two challenging wickets, a lot of seam and swing movement throughout.
"I know there's a huge amount of ability in our top five, so it's not a worry for me."