What might have been a relatively comfortable conclusion to the match from England's point of view became increasingly stressful, then hopeless as Morgan, Root and wicketkeeper
Jos Buttler all threw away their wickets.
All three fell to catches while trying to accelerate the scoring and while ignoring ample evidence that forced shots on a slow pitch were immensely dangerous. After hitting three fours and a six, Morgan drove a ball from Faulkner to Shane Watson at mid-off; Root seemed prepared to stay until then end but then played a blind, ramping shot and was caught by Xavier Doherty off Faulkner and Buttler pulled a ball from Coulter-Nile directly to McKay on the square leg boundary.
Bopara and Tim Bresnan (13) nudged England a little close to victory before Bresnan was wastefully run out with 24 runs still needed. Broad was then bowled by McKay for 7, becoming the eighth man out with 14 runs required from 18 balls.
"We should have got over the line there," Cook said. "We got ourselves into some good positions. Credit to Australia, at the end they held their nerve better than we did but we didn't help ourselves. There were some poor shots played under pressure.
"We did some very good things to get into a winning position and there were two other games in the series we could have won. Instead it's 4-1."
Earlier, Broad and Stokes shared six wickets as England restricted Australia to 217-9 in 50 overs.
Broad bowled opener
Aaron Finch (7) and Wade (31) and dismissed allrounder Watson for a duck to finish with 3-31 from 10 overs. Stokes removed March, Bailey for the innings' top score of 56 and
Glenn Maxwell for 22, severely denting Australia's batting effort and finishing with 3-43.
Bresnan bowled returning captain Clarke for 8 and Jordan claimed the late wickets of Faulkner for 27 and Coulter-Nile with consecutive deliveries in the last over but was denied a hat-trick by Doherty.
Bailey's 56, which included a half century from 60 balls, gave stability to a flimsy Australian innings. He put on 58 for the fifth wicket with Maxwell in the innings' most productive partnership, helping Australia recover from 64-4. Bailey and Wade then put on 55 for the sixth wicket, lifting Australia to 167-6 in the 40th over but sound late bowling helped England regain the upper hand. After Bailey was out, Australia lost four wicket for 48 runs.
Faulkner was later named man of the match for his outstanding bowling at the death and opener Finch was named man of the series.
