The reaction was quite positive in the Soviet scientific community, though still certainly muted or downplayed significantly to the public at large. In the press, much more attention was definitely given to the Soviet unmanned Luna exploratory probes than Apollo, but there was no question or hiding of the fact however that the first manned landing on the Moon was obviously a monumental achievement, and the scientific minds in the USSR certainly recognized it as such. The story was duly reported by the state-run press to the Soviet citizens, and they presented the facts to the public accurately, but were sure to downplay it and sell it to the citizens of the USSR as a victory for humanity, not merely for the USA.

There is a decent account of the Soviet scientific, political, and press reaction to the Moon landing in a NASA document published at the end of 1969 that was titled "NASA's Astronautics and Aeronautics, 1969 - A Chronology on Science, Technology, & Policy". Here is a link to the document, in PDF format.

In this document, which tracked national and international news stories related to space program activities, it states the following chronological breakdown during and initially following the Apollo 11 mission, beginning on page 233 of the PDF file.

July 16: U.S.S.R. radio and TV gave factual accounts of Apollo 11 launch but maintained third day of silence on Luna XV [the Soviet unmanned probe also headed for the Moon at the same time]. Major Soviet news program at 8:30 pm Moscow time showed tape of Apollo 11 liftoff taken from live comsat coverage.

Immediately after the successful touchdown of Apollo 11 on the Moon, this same document contains the following breakdown of Soviet reaction (on page 241 of the PDF file)

July 20-21: Soviet Premier Alexsey Kosygin complimented U.S. on lunar landing and expressed interest in widening U.S.-U.S.S.R. space cooperation during July 21 Moscow discussion with former Vice President Hubert H. Humphrey, who was ending Soviet visit. Soviet TV did not carry live coverage of Apollo 11 lunar landing July 20; Tass announcement was read by newscaster and carried in two-paragraph item on Pravda's front page. Evening paper, Izvestiya, accorded story more space and featured photo of astronauts on the moon. On TV, Cosmonaut Konstantin P. Feoktistov described landing as "major landmark" and said crew has coped "brilliantly" with mission. Georgy Petrov, Director of Soviet Institute for Cosmis Research, called Apollo 11 "outstanding achievement" but said more data per ruble could have been gathered by unmanned probes."

A few days later, on July 24th, after the Apollo 11 crew had safely splashed down in the Pacific, the same document (on page 252 of the PDF) reports the following -

"In U.S.S.R. TV viewers had live coverage for first time during mission at Moscow TV station hooked into Eastern Europe's Intervision network for live transmission of astronauts being deposited on carrier Hornet. Later, station devoted first two-thirds of final newscast to Apollo 11 and announced that Soviet President Nikolay V. Podgorny had sent telegram to President Nixon offering "our congratulations and best wishes to the space pilots."

"Soviet Academy of Sciences president Mstislav V. Keldysh called voyage "a big contribution to space exploration and further progress of world science." Cosmonauts send message to Apollo 11 crew: "We... closely followed your flight. We wholeheartedly congratulate you on the completion of your wonderful journey to the moon and safe return to earth."

Sergei Khrushchev, who is the son of Soviet Premier Nikita Khrushchev, has been interviewed about this very subject by Scientific American, and here is a link to the Q&A article where Sergei talks about Soviet reaction to the American success of Apollo 11 that you might find interesting.