And the Apollo program was hardly a poster-child for capitalism: federal government-run program, very centralized and partly militarized, very wasteful and expensive, at a time when marginal rates of taxation where above 70%.
Let's be honest: massive technological pushes that do not deal with production efficiency have nothing to do with capitalism or even democracy.
Ironic that it was Communism that beat us at every milestone except for the last one, and only due to an accident of history (the death of the leader of the Soviet space program just before a push for a moon mission and the lack of someone to fill his shoes).