The early stages saw both sides trying to show attacking intent, without being able to string too many passes together.
Goal attempts were few and far between, with England skipper Steven Gerrard trying his luck from distance on a couple of occasions, being unable to extend keeper Rais M'Bolhi.
Just past the half-hour mark England's best chance fell to Frank Lampard, after an Aaron Lennon cross had deflected off Emile Heskey, but the Chelsea man's low drive from 15 yards was saved by M'Bolhi, who then dived on the loose ball.
Barry and Wayne Rooney both found M'Bolhi with long-range efforts as a poor first 45 minutes drew to a close, with Algeria having enjoyed plenty of possession without creating any openings.
The second half began with England showing a little more intent, but woeful efforts at crosses from Heskey and Gerrard saw two openings go to waste in the opening ten minutes.
Just before the hour mark Jamie Carragher was booked, meaning that he will miss the final Group C clash with Slovenia, before Capello brought on Shaun Wright-Phillips for the ineffectual Aaron Lennon.
Twenty minutes from time Heskey passed up a half-chance when he opted to try to find Rooney rather than shooing on goal and England's only on-target attempt in the second half saw Gerrard's weak header collected by M'Bolhi.
Capello threw on Jermain Defoe and Peter Crouch in a bid to find a late breakthrough, but the former's long-range drive over the top was the closest England came to an undeserved winner.