How sudden was the eventual realization?
For example of other countries of the Warsaw Pact, the Polish people "got it" on 24th June 1976 when huge price increases were announced that lead to massive protests and rioting, whereas in Romania it happened more gradually, starting in 1978 but getting really dire only in 1982 when wages started getting withheld.
How many people were in disbelief of the acknowledged economic problems when the Perestroika began?
A major difference between the USSR and Eastern bloc countries like Poland is that price and wage changes were directly related to a situation where the regimes had borrowed heavily from Western countries, and faced balance of payments crises over their foreign debt.
In Poland's case, this was some $40 billion total, borrowed from such institutions as the IMF, World Bank, and London Club of private bankers. The situation in the 1970s was that Eastern bloc states seemed to be relatively safe investment opportunities, and the regimes in these states needed to borrow from abroad in order to finance imports of consumer goods, as Eastern exports alone were not able to finance these needs. In Poland's case, under First Secretary Edward Gierek, the new financial pipeline was a means of expanding social insurance programs and freezing food prices, but it also meant that Poland increased its foreign debt by 3,000 percent, and that by the late 1970s one third of Polish foreign debt was used to subsidize domestic consumption.
The whole socialist Eastern bloc's debt (minus Romania) increased from $6.1 billion in 1970, to $66.1 billion in 1980, and $95.6 billion in 1988. Romania is an exception because it managed to pay off its foreign debt - Ceausescu had much more means to implement a harsh austerity program in the 1980s. The debt was not only increasing, but increasingly unsustainable - a loan of one billion Deutschmarks to Hungary in October 1987 (tied to promises of economic "reform") ended up being immediately spent, with 2/3s going to interest payments and the remaining third spend on consumer goods purchases. The German Democratic Republic was spending something like 60 percent of its export earnings to cover debt payments. Ultimately, even to Eastern European security officials and economists realized that price controls could not last as the need to repay external debts built up.
The USSR was a very different situation, in part because it was able to finance itself with oil exports. The USSR had identified five dozen domestic oil fields in the 1960s, and in the course of bringing them online went from a net oil importer to an oil exporter. This timing was fortuitous as the Soviets were able to take advantage of the big oil price hikes following the 1973 Yom Kippur War, and between 1973 and 1985 oil accounted for 80 percent of Soviet hard currency earnings.
The Soviets even had a double boon from rising oil prices, in that they managed to profit from other oil exporting countries' earnings, specifically those oil exporters who were clients of the USSR, such as Libya, Iraq and Algeria. These countries invested much of their profits into the other big Soviet export industry - weapons sales. In this sense, the 1970s was a very different period for Soviet citizens - oil revenues funded higher salaries, more perks, the acquisition of certain Western technologies for producing consumer goods, Western feed for Soviet livestock, and for subsidized food prices. While Gorbachev labeled this the "Era of Stagnation", its worth noting that for most of this period, the Soviet economy continued to grow, albeit at ever decreasing rates.
The main issue was less that living standards weren't better than in previous years, but that the gap in living standards between the USSR and advanced Western economies wasn't closing, and this was increasingly apparent to members of the Soviet elite who traveled or were posted abroad, notably to Gorbachev, who traveled in Italy in the 1970s, and Alexander Yakovlev, who was Soviet ambassador to Canada at that time. Soviet industries used massive amounts of energy inefficiently, and oil field outputs in Siberia began to decline in 1983. Although output recovered in 1986, international oil prices plummeted in that year by 69%.
Around this time, Gorbachev likewise sought foreign loans to finance the purchase of Western machine tools and the like, and Soviet foreign debt began to explode, reaching some $56.1 billion by 1991. As I describe in more detail here, the overall Soviet economy began to unravel as various reforms were attempted under Gorbachev to kickstart output, but which in fact made the centrally-planned economy more chaotic and dysfunctional (and compounded so by new political crises). Government debt ballooned, and was paid for by printing money, which caused increasing inflation and a lack of goods in the stores. Most price controls in fact weren't lifted until January 1992, after the USSR fell apart.
So the short answer is that Soviet citizens who were in the know and had the level of security clearance to travel abroad would see that Soviet living standards were not catching up to the West in the 1970s. But the average Soviet citizen was still better off than they were previously at that time, and would only really start to see major hardships as the economy disintegrated starting in 1989. And with greater press freedom under Glasnost, they would be extremely aware of the dire state of affairs.
Sources:
Tony Judt. Postwar: A History of Europe Since 1945
Stephen Kotkin. Armageddon Averted: The Soviet Collapse, 1970-2000