Cook won the toss and elected to field in the first of four one-day internationals between the countries on Wednesday, and that appeared to be a good decision when the tourists were reduced to 19-2 early on.
However, Ajinkya Rahane (41) and Rohit Sharma (52) settled India down before Raina racked up a century of two halves - calm and measured at first, followed by a spell of destructive attacking - off 75 balls.
Raina was ably assisted by his captain Dhoni (52 off 51 balls) for much of his knock as India posted an imposing 304-6 off their 50 overs.
England simply did not have the firepower to trouble that total in damp, drizzly conditions - debutant Alex Hales top scoring with 40 as Ravindra Jadeja (4-28) led India's spin attack to dismiss the hosts for 161 off 38.1 overs.
That was enough to earn India a 133-run Duckworth-Lewis victory after a slight rain delay preceded England’s reply - and Cook was left in little doubt as to who did the damage.
"We didn't play very well - credit to MS Dhoni and Suresh, they took the game away from us," Cook told Sky Sports.
"But when we were batting, this wasn't a 160-run pitch.
"We need to dust ourselves off and go again. We won't win many matches playing like that."
Cook went on to indicate that seamer Chris Woakes (4-52) and Hales were the only England players to come out of the game with any real credit, while also offering words of support for bowler Chris Jordan, who gave away 12 wides in his figures of 0-73.
"Chris Woakes played pretty well and it’s nice to see Alex Hales get off and running," he added.
"CJ's [Jordan] had a really good start to his international career [and] he'll learn from it."