It is one of the most famous Olympic moments in the USA and the American team was treated like heroes, but I am wondering what the response was to the Soviet national team losing to the huge underdogs.
In short, no.
The Miracle on Ice was not the first major Soviet loss in hockey, and may not even have been their biggest upset: at the 1976 IIHF World Championships the Polish team defeated the USSR (which was largely comprised of the players that would play in the Miracle on Ice) 6-4; for reference, at the 1976 Olympics the USSR defeated Poland 16-1, and had won 12 of the past 13 World Championships. When the IIHF (world governing body of ice hockey) published a list of the 100 greatest international stories for their 100th anniversary in 2008, this game was ranked as number 39 (though the Miracle on Ice was #1).
As well, the majority of the Soviet team would continue to play in international tournaments throughout the 1980s, winning gold at both the 1984 and 1988 Olympics, and six World Championships out of a possible nine before the collapse of the USSR (and medals in the other three years), as well as the 1981 Canada Cup (international tournament hosted by the NHL that was "best-on-best"; NHL professionals were allowed to play, which they couldn't in the Olympics until 1998).
As for Viktor Tikhonov, the coach, he remained as coach of CSKA Moscow until 1996. Backed by the Red Army, he was able to continue the practice of drafting good hockey players into the military so they would have to play for his team; they won 13 consecutive domestic titles (1978-1989); Tikhonov also remained as the national team's coach until 1994, winning the tournaments mentioned above.
None of this suggests that there was any reprimand by the government. Whether Tikhonov, who has/had a reputation of utilising a dictatorial style of coaching, punished the players is something I can't properly comment on under the subreddit rules; however I will note that CSKA and national team players (who were often one and the same) were confined to barracks for eleven months of the year, forbidden to see their families, and trained extensively in that time. It would not be unusual if Tikhonov further restricted the players freedoms after such a loss.
Vladislav Tretiak, the Soviet goaltender pulled at 19:59 of the first period in that game, wrote a book called Tretiak the legend. In the chapter focusing on Lake Placid he devotes little time to returning home but does say:
"When our plane landed at the Moscow airport, the crowds came to meet us and carried some of the other athletes away on their shoulders. The skier Nikolai Zimyatov was the major hero of the Olympics that year. We were demonstratively shoved aside and lefe unnoticed. And rightly so!"