Democracy? Vilified? Quite the opposite.

The preamble to the 1977 constitution says

It is a society of true democracy, the political system of which ensures effective management of all public affairs, ever more active participation of the working people in running the state, and the combining of citizen's real rights and freedoms with their obligations and responsibility to society.

Article 9 says

The principal direction in the development of the political system of Soviet society is the extension of socialist democracy, namely ever broader participation of citizens in managing the affairs of society and the state, continuous improvement of the machinery of state, heightening of the activity of public organisations, strengthening of the system of people's control, consolidation of the legal foundations of the functioning of the state and of public life, greater openness and publicity, and constant responsiveness to public opinion.

It was common for Soviet politicians and media outlets to praise the system of Soviet democracy.

For example, in 1950, Stalin released a statement on International Women's Day:

Soviet women are taking an active part in administration and in state building, which in itself is a vivid proof of the genuine democracy of the Soviet system: 277 women have been elected Deputies of the Supreme Soviet of the U.S.S.R., and more than 1,700 to the Supreme Soviets of the Union and Autonomous Republics; about half a million women are Deputies to local Soviets.

When Stalin was running for election to the Supreme Soviet in 1937, he gave a speech in Moscow to voters in which he said:

The forthcoming elections are not merely elections, comrades, they are really a national holiday of our workers, our peasants and our intelligentsia. Never in the history 0f the world have there been such really free and really democratic elections—never! History knows no other example like it. The point is not that our elections will be universal, equal, secret and direct, although that fact in itself is of great importance. The point is that our universal elections will be carried out as the freest elections and the most democratic of any country in the world.

Far from criticising the Western world for its democracy, the Soviet Union criticised it for (alleged) lack of democracy. Stalin, in an essay promoting the new constitution that was to be adopted, said:

Democracy in capitalist countries, where there are antagonistic classes, is, in the last analysis, democracy for the strong, democracy for the propertied minority. In the U.S.S.R., on the contrary, democracy is democracy for the working people, i.e., democracy for all.

I've only quoted Stalin here, but these comments pretty well represent the general thrust of Soviet rhetoric throughout its existence. The Soviet system of democracy was praised as more truly democratic than that of the capitalist countries; "bourgeois democracy" was considered to be a sham that concentrated power in the hands of the capitalist class, while giving the illusion of public decision-making. By establishing property relations along collective, socialist lines, the Soviet Union eliminated the capitalist class, thereby removing this defect of the capitalist countries and allowing for the creation of a "genuine democracy".

The criticism of the capitalist countries was not on the basis that they were democratic, but on the basis that they were capitalist. Marxism holds that capitalism (and imperialism, another crime that the West was charged with) is a system of exploitative relations.

The USSR villified capitalism, not democracy. The USSR actually considered itself more democratic than western democracies, who were considered to be under opression from the upper ruling class. Indeed, while American propaganda oftentimes villified the Russian people, for the most part Soviet propaganda considered the American people hostages that needed to be freed from their capitalist masters.

Theres a quote from a Soviet citizen during the cold war that went something like "Everything they told me about the Soviet Union was wrong, but everything they told me about the United States was right." I think it's a pretty apt descriptor of the propaganda used on both sides of the cold war

'Bourgeouis democracy' such as that of the US was and still is vilified by communists, though mainly because it isn't seen as true democracy.

Though these are of course from Cuba in the early sixties, I think these quotes from Che Guevara illustrate this viewpoint pretty well:

Democracy cannot consist solely of elections that are nearly always fictitious and managed by rich landowners and professional politicians

We should not allow the word "democracy" to be utilized apologetically to represent the dictatorship of the exploiting classes.

In USSR western democracies was never dubbed so. They were called "imperialist" and "capitalist" powers and thus were vilified fiercely.

Related: was 'democracy' defined the same in the USSR as in the USA?

If I'm not mistaken, "democracy" in theory and practice was celebrated even in Marxist autocracies. It wasn't pure democracy (arguably, no democracy is a pure democracy) but at the local level, representatives to communist governing bodies were elected through a democratic process, even if the selection and grooming of these individuals wasn't really an organic or democratic process. This is true especially of China, where an authoritarian structure at the top allows democratic expression at the local level, as channeled and constrained by those structures.

Even in inarguably autocratic, anti-democratic marxist states like North Korea and the Congo would pay rhetorical homage to the theoretical popularity of democracy in the naming conventions of these states (Democratic People's Republic of Korea, Democratic Republic of the Congo, etc. - Soviet satellite states are infamous for this).

This gets to the heart of a broader debate. The ideological battles of the cold war weren't predicated upon a struggle between "democracy" and "authoritarianism", but rather a struggle between competing economic arrangements - market economies versus centralized economies. Framing the debate in terms of political arrangements highlights tangential differences between western and eastern powers (in this case, cultural/political attitudes towards freedom of franchise and expression) that naturally inflame the very closely felt passion for free speech/expression and the vote, particularly in Americans, who by nature and heritage are quite individualistic. These passions are not as closely held or cherished in Eastern nations, where political heritage tends towards paternalism and individualism is seen as unorthodox. In this way, framing the debate as "democracy vs. autocracy" was a convenient way to enlist westerners who otherwise might have sympathies towards the potential benefits of socialist practices in an ideological struggle as opposed to an economic one (and also to elide the nominally democratic practices entrenched even in communist nations) that they might not have been as fired up about and in so doing, get people to support domestic economic policy inarguably hostile towards the working class. Not to get all Metal Gear Solid 3, but the cold war was about money, not the flag.