And please take note, it's impossible to speak for a group of people or boil down what's happening to anything concrete when it's very disparate and unique to each individual. But I'll point out a few trends I've seen.
For some background, eastern Ukraine is very pro-Russian, and was (and is) very pro-Yanukovytch. The majority of the people I talked to pined for the days of the Soviet Union, when bread was cheap, everyone had what they needed, etc. They viewed the fall of the soviet union as a psychological infiltration from the west, and, apart from a short rendezvous to defeat Hitler, the west is still the enemy and full of corrupt capitalist blood suckers (which, to be fair, can be not-too-far from the truth at times). It's hard for most westerners to imagine that many of the major cities in Ukraine have a 30 ft + statue of Lenin or that many of the major streets are named "Lenin" street, but it's not uncommon for me to see poems or images praising Stalin from my Russian Facebook (or Vkontakte) friends. The Soviet Union was the good ol' days, not grouped together with pre-WWII Germany as it often is in the States. Stalin is decidedly not Hitler. I include this information not to say that anti-protest comments come from Soviets/Communists, but the influence of the Soviet Union and how information was relayed still lingers, even today.
When most of the people there, especially the older generations, talked about the media, they would often reference a transmission from Moscow (передача из Москвы) as the only source of reliable information. Think of it as "published in the New York Times." And bear in mind that the New York Times has been just as involved in Propaganda as was Pravda in its heyday.
The battle, in the mind of Russians, is one of information, and of each side trying to deceive the other. Americans look at pro-Communist posters as "propaganda" but at the western side's as simply "promotional posters." Russians see it as an ideological battle being fought with information.
For many Russians this is the same battle being fought. It's not revolutionaries vs. evil dictator, it's east vs. west. It's Russia vs. the Europe/United States. And when a battle of information leads to such sharp contrasts, you defend your side, in a similar way to how Republicans defended George Bush when he did stupid things and Democrats defend Barack Obama when he does stupid things. It's not about the particular circumstance, it's about ideology. You'll notice a common thread of "Well, sometimes Russia sucks, but America sucks sometimes too." Which, again, is completely fair. And again, this is not something that only happens in Russia.
But this leads to trying to sway the facts in favor of one side, and that often leads to gross misinterpretation of what is actually going on. Russia Today and Pravda are state-sponsored PR organizations dressed up as journalistic institutions. When the protests began, according to RT it was "a handful of people" gathered, angry at "a failed trade law," and not the bubbling over of frustration as a completely corrupt President threw his enemies in jail and deepened relations with Putin.
Take, for example, the naked protestor who was mocked by police, photographed, slapped, kicked, and put in a van (graphic video:) http://www.youtube.com/watch?v=oSt4kAItj4Q. Many of my Russian friends would tell you he was trying to set himself on fire, the police saved him, took pictures "in memoriam," gave him a few friendly slaps, and let him go. They would leave comments like "Let him burn next time!" or "Be careful, police, you're only giving the terrorists more psychological ammunition!"
So, to answer your question, in the mind of a Russian it's because we're still fighting a war of information, and the west likes to deceive and destroy Russia psychologically. They defend their ideology the same way we defend ours, and sometimes information and facts are left out to dry.