First paceman Lasith Malinga took three for 50 as Sri Lanka restricted England to 219 all out yesterday.
Then, after Sri Lanka had wobbled at 62 for three, fifties from Mahela Jayawardene (53) and Lahiru Thirimanne (60 not out), together with captain Angelo Mathews's 42 not out off 34 balls, saw the tourists home with 10 balls to spare.
But there was a controversial moment during England's innings when Sachithra Senanayake ran out Jos Buttler as the non-striker backed up.
"You would have to ask Angelo Mathews," said Cook when asked for his view of the run out during the presentation ceremony.
"We were obviously disappointed. I hope I wouldn't do it.
"You don't know in the spur of the moment how you would handle it."
However, Mathews insisted: "He was taking starts, not only this game but in the last game as well.
"We gave him two warnings, and I don't know what else you can do to stop him doing that, so we had to go for it.
Sri Lanka, set a seemingly modest 220 for victory, were cruising at 55 without loss in the eighth over as Tillakaratne Dilshan got after the England seam attack.
But their charge was interrupted by off-spinner James Tredwell's burst of two wickets for four runs in 11 balls.
First he had Dilshan, whose 28 featured five boundaries, caught off a flashing drive by Joe Root at extra-cover.
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