There is of course a danger in discussing how a continent performs since there is just as much variation in the more successful continents than there are in the less successful ones. Also, it has to be remembered just how difficult (and rare) to win a World Cup. 8 different nations have won the World Cup (3 from South America and 5 from Europe). To put this in context, 166 countries entered qualification for Brazil 2014.
So perhaps it's worth considering the performance of African countries from a different perspective. That there are fewer African teams reaching the later stages of the World Cup may be due to them having fewer teams entering the World Cup finals. In the four tournaments since 1998 there have been 5 African qualifiers (in 2010 there were 6 because South Africa were hosts). Prior to that there were 3 in 1994, 2 in the three tournaments to 1990 and 1 in the three tournaments in the 1970s. Apart from an appearance by Egypt in 1934 there were no African participants prior to 1970.
In next year's finals in Brazil there will be 5 African nations from 52 qualifiers, while Europe will have 13 from 53 qualifiers. Asia will have 4 from 43 qualifiers (presuming Uruguay beat Jordan), North, Central America and the Caribbean will have 4 from 35 (assuming Mexico beat New Zealand) and finally South America will have 5 from 9 (plus the hosts Brazil making it 6 from 10).
Africa, despite having more than 5 times as many nations, have the same number of qualifiers as South America.
Africa's record at World Cup finals is not as poor as popular myth may suggest. With a similar representation as South America their teams do relatively well. Brazil and Argentina fly the flag for South America and without them the record for South American since the 1980s is not strong. Since 1986 at least one African nation has qualified from the pool stages and as noted earlier 3 have qualified for the quarter finals. In the same period 4 different South American nations have qualified for quarter finals. Excluding Brazil and Argentina, only Paraguay and Uruguay have reached the last 8 since 1986, and both of those in the most recent World Cup in South Africa 2010.
If South America's high proportion of finals places if based on FIFA ranking then there is something of a circular logic, as rankings are boosted by performances against other higher ranked teams. Appearing at the World Cup final provides further boost to rankings. The table below however shows the number of nations from Africa and South America in the top 30 FIFA ranking spots each December since 1993 (the 2013 figure is for October).
The division of FIFA into separate federations creates a situation where each federation looks to protect their own and this can mean persistent under or over representation by nations in those federations. In the current qualification Australia moved from Oceania to Asia because the Oceania representatives must go into a play-off with the fifth South American nation and in a two-legged tie this is a big ask for a nation from Oceania.
A rebalancing of the representation of each federation may be warranted to encourage nations in football's developing regions. Perhaps adding South America to Central, North American and Caribbean. However, politics will dominate and there is likely to be conflicting national, federation and FIFA objectives.