Sri Lanka lost the fifth and final ODI by 122 runs in Cardiff on Saturday as England took the series 3-0, with one tie and one no result, following their 2-0 success in the preceding three-Test campaign.
England, sent into bat by Mathews in the Welsh capital, made 324 for seven with Joe Root (93) and Jos Buttler (70) putting on 109 for the fifth wicket.
Sri Lanka never looked like chasing down a target of 325 and were bowled out for 202 with 44 balls to spare.
Dinesh Chandimal (53) and Danushka Gunathilaka (48) were the only Sri Lanka batsmen to make much impression Saturday, with left-arm quick David Willey (four for 34) taking wickets at both ends of the innings.
Sri Lanka, whose two wins this tour have come in a pair of one-day internationals in Ireland, will have one last chance for a victory on English or Welsh soil on their current trip when they face England in a lone Twenty20 at Southampton on Tuesday.
"There will be good times as well as bad," said Mathews, who became Test and one-day skipper in 2013 before taking on the T20 leadership just before this year's World Twenty20 in India.
"This is a tough time for me as a captain and for the whole unit but you can't run away from it," added the 29-year-old all-rounder.
"I'm pretty sure if we keep improving day-by-day we can come out of this hole," he insisted.
"For the past two months we've been having the same problems, either batting bowling or fielding has let us down in every single game.
"Especially in the one-dayers we needed a perfect day to win against England.
"We didn't have that perfect game and we paid the price."
"Congratulations to the English boys, they put us under a lot of pressure and didn't give us the slightest of chances. They outplayed us in all three departments."
Last year, Sri Lanka thrashed England by nine wickets at the World Cup in Wellington but since then batting greats Kumar Sangakkara and Mahela Jayawardene have both retired.
Mathews, asked if he had been surprised by England's progress, replied: "A few years back they were in the same situation as us, a rebuilding phase and they have stuck to their plans, they've stuck to their players and now you can see the results.
"They've been playing some fantastic cricket and are very competitive outside England as well."
England, particularly in Test campaigns have had a habit of losing matches when a series has already been won.
But they were ruthless in Cardiff, to the delight of white-ball captain Eoin Morgan.
"It was a very convincing performance," he said. "There was no let-up at all really."
Yet it might have been all so different had not England, who were 82 for six chasing 287 to win, escaped with a tie in the ODI series opener at Trent Bridge on June 21.
"It was brilliant to come out of that game without being wounded," said Morgan.
"I thought that was a great effort."
Buttler's quickfire 45-ball innings on Saturday saw him become the latest England batsman to make an impact against Sri Lanka and a delighted Morgan said: "He's been outstanding...He's fronted up every time he's been asked."
England bat long in ODIs with Adil Rashid, who has made several first-class hundreds, their last man in.
"Knowing that Adil is at number 11, a fantastic batsman as well, it gives you that licence to push your gamble button and try to kick on a bit earlier," said Buttler.
"It doesn't mean you're trying to pass your responsibility, but it's good to know that there are guys behind you who can pick up the baton as well," he added.
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