"Definitely (a win would be on our mind). You can't go into that game with that (draw) mentality. We have to do same as we have done in these last two games (at Mumbai and Kolkata). And again, produce the goods," said Cook.
"We know we can do something special, but it will need a lot of hard work to do that," he added in the post-match media interaction.
Cook said that his team has put in lot of hardwork to turn the tables around after they went down in the opening Test match to India in Ahmedabad.
"What we have done really is take what we did in the nets out in the middle. We have started to perform close to our potential. That's what really happened in this game.
"Our bowlers have been outstanding in that first innings to restrict them (Indians) to 300 on that wicket, and that was a great effort.
"Yesterday, when they were 80 for nought, to put in a session like we did yesterday afternoon when we took six wickets was high-skill bowling," Cook said.
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England took six wickets for 36 runs in the post lunch session yesterday with Graeme Swann giving the breakthrough with in-form Virender Sehwag's wicket.
"The spinner at one end, Swarney getting Sehwag straightaway and then the reverse swing from Jummy. It was exceptional. What we've done is play close to our potential in the last couple of games. That's why we have won." (MORE)