It's also worth noting that the Soviets were somewhat divided on a manned moon mission in the first place.
Many within the space program and the politburo viewed a manned moon mission as a waste of money, and believed that the same data (if not even more) could be obtained cheaper and much more easily through probes and rovers. The Soviets were, in fact, quite advanced in that area. The Lunokhod rovers of the 1970s set some records that NASA has just recently broken.
Khrushchev, however, demanded that an attempt take place. He was all about racking up "firsts" for the Soviet space program, but also refused to consistently, and sometimes even sufficiently, fund the program.
It's worth mentioning, as well, that the Soviets didn't really have one unified space agency until 1964. There was a lot of internal competition from rival design companies, which tended to confuse and muddle affairs.
After the Americans put a man on the moon, the propaganda value of a Soviet landing was seriously diminished, so they focused their resources elsewhere, with some success. They were decades ahead of NASA in space stations, for example.
Two main reasons. One was that the rocket engine they had planned to use , the N1, was not successful. It just was not reliable. You can YouTube the explosion, it's pretty spectacular. The second reason was that it was no longer worth the cost. The "reward" for getting there first was huge, and the Americans won that prize. The prestige for getting there second was much less.
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