Coach Gordon Igesund had hoped for two resounding performances in the build-up to this month's tournament to rally support behind his beleaguered side but South Africa finished a second consecutive game without scoring.
Only 14,558 attended the match at the Orlando Stadium, reflecting a general discontent with the team's performance after they lost 1-0 to Norway in Cape Town on Tuesday.
Saturday's showing did little to dampen fears that the tournament, which kicks off next Saturday, will attract poor crowds.
South Africa open the finals with a match against the Cape Verde Islands at the cavernous Soccer City in Johannesburg.
Algeria, who played a cautious game despite being the second-ranked side in Africa, had three chances in the first half-hour but put them all wide while the home side took 39 minutes to create their first attempt on goal.
Algeria's Rais Mboli pulled off a good save from Bernard Parker just before the break but it was the only real work of the night for either goalkeeper.
Algeria's first game at the finals is on January 22 against Tunisia in Rustenburg.