Brian Eastick's side were impressive in their final Group B game in the Czech Republic but Italy's victory over the hosts rendered England's result immaterial.
England needed to win and for the Italians to drop points and did their job well with goals by Ben Mee, Freddie Sears and Daniel Sturridge.
But the Azzurri's 4-3 win ensured they progressed to meet Germany or Hungary in the last four.
Eastick's team began brightly in the competition but struggled after Carroll picked up a foot injury in training and had to return home.