Djamel Belmadi’s side saw their unbeaten run stretch to 35 matches, within two of Italy’s world record 37 game streak, but that was the only real positive after a disappointing display.
Algeria won the cup for the first time since 1990 when beating Senegal in the final three years ago and are among the favourites to repeat the success but, like the Senegalese, who needed a stoppage-time penalty to overcome Zimbabwe in their first game, the holders found their opener hard work.
Though the favourites dominated possession, it was Sierra Leone that had the better opportunities in the opening half, played on a testing surface at the Japoma Stadium in Douala, Alhaji Kamara going closest with a low strike that just beat the near-post.
Kamara did find the net after the restart but the effort was rightly chalked off for offside as Algeria began to increase the pressure.
Yacine Brahimi missed a glorious chance after good work from Islam Slimani and Riyad Mahrez, before a wonderful block from former England international Steven Caulker denied substitute Sofiane Bendebka what had looked an open goal.
Mahrez was then denied by a superb save from Mohamed Kamara in the Sierra Leone goal before West Ham’s Said Benrahma wasted a wonderful chance to win it moments after coming off the bench as he scuffed wide from ten yards.