Alastair Cook has admitted that England simply "need to score more runs" after a six-wicket defeat to Sri Lanka saw them lose the one-day international series 3-2.

The hosts managed only 219 all out at Edgbaston on Tuesday, a total which the Lions knocked off with more than three overs to spare after recovering from 66-3.

Cook confessed that he and the rest of the top-order batsmen are culpable for England's failure to win the first series since the reappointment of Peter Moores as national coach, for not converting what have often been cautious starts into match-winning scores.

Jos Buttler's record-breaking century at Lord's from number seven was the only time that an Englishmen reached three figures in the five matches, which is a statistic that concerns captain Cook.

"We need to score more runs," he told Sky Sports News. "The batters haven't been in the greatest of nick in this series with only one hundred and no one has really carried us through so probably the batting has to be an area of a bit more concern.

"We were probably about 20 or 30 short. They bowled pretty well on that wicket. It was quite slow and it suited them. If we'd have got 250 on that wicket they'd have found it quite tough to chase it down because we bowled pretty well there.

"On a slow wicket we got off to a good start. Everyone got in. We got 10s and 20s but if you're going to win a game of one day cricket batting first you need two of those guys to go on and get 80s and 100s. That's what sets up one day wins."

England name the 12-man squad for the opening Test against Sri Lanka on Wednesday.