The triumph at The Oval earlier today secured a 3-1 series win for England, following on from success in Southampton, Manchester and London to overcome an early 1-0 deficit.
"[It was] an amazing turnaround," Cook told Sky Sports News. "After Lord's to have won like we've won the last three games, the guys can take a huge amount of credit.
"All summer before we won at Southampton we played cricket in patches. We played good cricket and then let it go in an hour or so.
"To maintain the pressure on India like we did in these three games, that last hour here showed that – [India] crumbled at the end but that was down to relentless pressure."
The 244-run result is England's second-biggest win ever against India.