Centuries from Jonathan Trott and Ian Bell secured a draw in the fourth Test in Nagpur and a 2-1 win in the series.
"It's a very special day for us, it's been a special tour and we'll have great memories," Cook told Sky Sports 1. "Today was a fantastic effort by Trotty and Belly. All right, it was a flat pitch, but how calmly they batted was fantastic."
He added: "We were slightly surprised how low and slow the pitch was, and it got better as the game went on.
"We knew when we batted in the second innings we had to make it very hard to take those wickets, so credit to our batsmen for fronting up and taking on that challenge."
The series success was all the more impressive after a heavy nine-wicket defeat in the first Test in Ahmedabad, which prompted widespread forecasts of a 4-0 series whitewash in India's favour.
"We didn't handle the Ahmedabad wicket as well but the others were all very different and we adapted well," said Cook.
"The bowlers have been brilliant and our batters have contributed big runs. Everyone in the squad can be very proud, especially after Ahmedabad and that heavy defeat.
"The guys who played a couple of games all made a difference and the amount of effort the guys have put in for me, I can't ask any more.
"It's always nice when it goes well but I can't praise the team enough. And the support we've had everywhere we've gone, not just from the Barmy Army but also the Indian public, has been fantastic."
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- Jonathan Trott