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England dominated the match throughout to win by 266 runs with Cook scoring 95 and an unbeaten 70 before Moeen Ali took six wickets in India's second innings to wrap up victory on the final day.
Cook said he was delighted with the way that all of his players had contributed, from opening bowlers Anderson and Stuart Broad to his specialist batsmen.
"It helps, doesn't it? One to 11, I thought we performed really well to a man," he said.
"And the guys who were slightly questioned at the beginning of this Test match really delivered.
"Obviously it was great to see Belly (Ian Bell) scoring a big hundred, it's amazing when you score, get big runs on the board, how much difference it makes.
"Especially from the top order, you're not ... you know, the lower order, it's great when they contribute but you set the game up like we did on that first day, 240 for two, you know you start getting ahead of the game and you can dictate it, and that's what we did."
Meanwhile, Anderson, who took seven wickets in the match, paid tribute to the way all of the bowlers performed to dismiss India for 330 and then 178.
"Obviously it helps when it swings, that's my strength, but at the same time, it swung at Lord's and we probably didn't quite get it right as a group," he began.
"I thought this week we were absolutely relentless as a four-seam attack. Everyone bowled brilliantly.
"(Chris) Woakes is walking out of the game without any wickets, but he bowled fantastically well, deserved some wickets and if he bowls like that again he will get them eventually.
"It's really exciting for us that we've set a benchmark as a team - that is our benchmark as a bowling attack, that is how good we can be, our job now is to maintain that throughout the rest of the series."
Dhoni, who was taking plenty of plaudits after a 95-run win at Lord's, had to face questions about whether his side's batting was now a concern.
He played down the lack of contributions in this match, however.
"Well, once it happens... it's not really a concern, it becomes a concern once it becomes repetitive, once it becomes a habit," he countered.
"Let's hope that it doesn't become a habit, and also the good thing that you can say is that the batsmen are getting starts.
"It's just a matter of time before they start working those starts into big innings and that's what is needed.
"Getting starts is more difficult than converting starts, you know, hopefully they'll get a taste of it and come back strong."
Video courtesy of SNTV
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