Was funding increased/decreased? Was space exploration still considered a priority?
I'm afraid I can't tell you about funding, but this graph shows that the number of USSR space launches per year grew until well into the 1980s, whereas NASA's launches decreased from 1965 onwards, which was around the time when Apollo 11's moon landing was almost certain.
This graph shows how the US's weight to orbit requirements dropped off after the end of the Apollo, but the USSR's increased steadily, showing that they were still very interested in their space program.
I think it's quite clear that, following the main research push for Apollo, NASA began to slow down the rate of launches and decreased their funding, but the USSR's space efforts intensified.
Wow! Actually a question that I can answer! Amazing! Cool!
The Soviet Space Programme (referring to the manned lunar programme, the effort to put a man on the moon –read the post below) was pretty much abandoned almost completely from the moment when the transmissions from the moon were broadcast. The N-1 rocket that was supposed to carry people to the moon was decommissioned to the extent of even being used as raw materials for pig-pens. Some of its NK-33 engines were saved, though, and they constitute some of the materials of the on-going litigation inside the US about the state of the space industry depending on Russian materials.
Many of the missiles that had a use as weapons survived, but the largest rockets, those used to go to the Moon and were too large to even be used as ICBMs were scrapped up pretty quickly.
A very interesting documentary on the matter: http://www.youtube.com/watch?v=MZnYr94aa9E
Edit: Spelling.
Edit two: Clarify what was meant by the programme, as suggested by /u/MarsMJD.
The two previous posts have already answered the question, but I found an anecdote I'd like to share.
Luna 15, an unmanned Soviet craft, was in lunar orbit at the same time as Apollo 11. Furthermore, Luna 15 impacted on the Moon while Neil Armstrong and Buzz Alrdin were still on the surface making preparations for their ascent back to the command module. Luna 15 crash landed at 15:50 UTC on July 21st; Apollo 11 commenced its ascent stage shortly thereafter at 17:53 UTC.
So it can be said that while the Soviet space program was imploding on the moon, the American space program had just reached its greatest heights.
Sources
The Soviet Manned Lunar Program
[Previously unheard recroding of Luna 15 landing released] (http://sservi.nasa.gov/articles/previously-unheard-recording-of-luna-15-landing-released/)
