Cook, however, was not ready to take things easy.
'We're not even halfway through this Test match yet. We have to keep scoring. Then we will put them under more pressure when they bat again. We know if we put a lot of miles in their legs again, as we have been doing in the last two Tests, it gives our bowlers more time to rest up.'
Cook said his aim now would be to add as many runs as possible to his overnight score, and maybe, chase a 'Daddy Hundred,' a phrase batting coach Graham Gooch uses instead of big centuries.
'We talk about trying to make Daddy Hundreds... is from Goochie and he doesn't really count anything under 150,' said Cook who hit his 19th Test century during the second day's play.
Cook, after failures in the first two Tests, came good here and he said it was due to the hard work he put in to improve his batting.
'I did a bit of work last week to get myself into better positions. I might have been falling over slightly but the conditions in the last couple of Tests were also very tough,' Cook said.
'It was important to get through the new ball. Fortunately, I was able to do it and make it count. It makes you forget the low scores.'
Cook singled out Praveen Kumar as the bowler to have troubled him the most in the series.
'Kumar has bowled exceptionally well. He has swung it both ways and found a good length as well. Fortunately, I survived him today. He has definitely been their best bowler.'
Cook is now just one short of equaling his friend and mentor Gooch's tally of 20 Test centuries.
'It will be a shame when, or if, I do equal him because he is a great player but he's also a friend now and I think that's important.
England have the most consistent side in Test cricket in recent times but Cook is not willing to rest on the laurels.
'It's nice but let's not get carried away. We have to keep working as hard as we have. You have a work ethic in our batters over the last couple of years since Goochie came on board.
'Since then results have gone through the roof but we have to keep our feet on the ground. We want to improve every time we play. Obviously the Ashes was fantastic and we are hitting those standards but we will never be satisfied with what we have done.
'This team wants to stay together for a long time and do something very special, and hopefully, we can continue doing that,' Cook said.