Although proud of what was, on the whole, a successful campaign, captain Aaron Finch said it was a shame his side had saved its worst performance of the tournament for the knockout stage.
"We got off to a flyer and when chasing a relatively small total, that's the difference".
England will head to Lord´s to play against 2015 runners-up New Zealand.
The decider will be just the third in 32 years not to feature Australia, with the Aussies also having only dropped the 2011 tournament since 1999.
England completely outclassed Australia as they secured their place in the final of the Cricket World Cup where they will face New Zealand at Lord's on Sunday.
"It started with the bowling performance and then the way they knocked that off was outstanding".
Adil Rashid claimed 3-54, including the wickets of Carey (46) and Marcus Stoinis, and Archer sent back Glenn Maxwell, who scored at a run-a-ball for his 22 before being deceived by a slower ball.
By that stage Australia were 3-14, and it was left to Steve Smith to lead a recovery mission.
Eoin Morgan celebrates as he scores the winning runs.
England, in reply, started explosively.
Although Bairstow was trapped leg before by Starc for 34 and Roy was wrongly adjudged to have hooked Pat Cummins behind, Root and Morgan were untroubled in an unbroken stand of 79.
"I can't believe I have just watched that", former England captain Alastair Cook said in commentary for BBC.
Michael Vaughan added: "It's remarkable and all the players deserve all the credit, the management, everyone involved in English cricket".
"(Jason) Roy's monster hitting encapsulated England's dominance and near-disdain for their opponents", Etheridge wrote.
The loss of England's opener did little to stop their charge towards to the final, as Root (49no) and captain Morgan (45no) clinched victory with a mammoth 107 balls spare.
A short ball from Archer struck new man Carey on the helmet and the Australian wicketkeeper had the presence of mind to catch his lid as it flew towards the stumps with the fiery delivery drawing blood from his chin.
Woakes (3-20) removed David Warner, Australia's leading scorer in the tournament, for nine and bowled Peter Handscomb who was making his World Cup debut as replacement for the injured Usman Khawaja.
Until Saturday's final round of group games, England were set to play India in this match.