It was much closer contest at Old Trafford on Saturday where a match of fluctuating fortunes saw England recover to make 268 for nine after Cook won the toss.
Sri Lanka then collapsed to 29 for three in reply, with opener Dilshan out for just four, before a sixth-wicket stand of 102 between Angelo Mathews (62) and Jeevan Mendis (48) gave the islanders hope of victory.
But it was not to be, seamer Jade Dernbach striking twice in two deliveries as England won with 10 balls to spare.Dilshan, who made 193 in the drawn second Test at Lord's only to have his thumb broken that innings, was deeply dejected by his own one-day series return of just 17 runs in five matches.
But he took heart from the likes of 21-year-old Dinesh Chandimal, who made 54 at Old Trafford and topped Sri Lanka's one-day series batting averages with 164 runs at 54.66 including an unbeaten 105 in a six-wicket win at Lord's.
"As a captain I didn't get any runs and I'm really disappointed with that," he said.
"We had a big issue in the last three or four years with the middle order not doing well for Sri Lanka.
"The top order was always getting runs but now we have more confidence in the middle order and that is good for the future. We can look forward to the upcoming series with the youngsters."
Cook was named man-of-the-series for a return of 298 runs at 74.50 including a career-best 119 at Lord's.
"He's scoring a lot of runs in Test cricket and he's come into the one-dayers with confidence," said Dilshan, whose side conclude their tour with one-day internationals against Ireland and Scotland in Edinburgh next week.
"He isn't a bad one-day player and batted really well for his man-of-the-series award."
England's next challenge sees them at home to India, the world's number one ranked Test side and the team that beat Sri Lanka in the World Cup final, for Test and one-day series starting later this month.
"India are playing good cricket in the last couple of years and England are also playing well," said Dilshan. "It will be a good series and I think it's a fifty-fifty call who will win."