I always remember it as the 21st day of July, which it of course it was to those who watched it in the early hours of the morning, in the UK.
The Americans set out to beat the Russians, and once that was done, they saw no point in continuing it. At least they agreed to finance a few more Apollo missions. I think it has to be said that Apollo 13 scared them badly, and it showed how the whole thing could publically backfire if something went wrong, as it would eventually. If they didn't dare risk sending any more people to the Moon, they certainly wouldn't seriously think about sending them to Mars.
From a technological point of view, it was indeed a matter of designing the minimum required to do the job. The on-board computers were built for the job. I wouldn't have wanted to fly an Apollo mission with Windows! If they had relied on one of those and it went wrong, they would have been lost. As it was, their on-board computers 'assisted' them, enough to provide a better chance of a safe landing and return. Good timing, gravity and the educated human brain did almost everything else required. It is only modern civilisation who imagines that nothing difficult can be done without a modern computer!