Well, Yanukovitch was pro-Russian. At least more than the rest of the political spectrum in Ukraine.
Yanukovitch was absolutely not pro-Russian, he was an opportunist backed by certain oligarchs, specifically those running the industrial concerns in the Donbass. These oligarchs were basically in favour of integration with the EU, since they wanted another place to make money off of. Thus, these oligarchs preferred Yanukovitch to any Western crook (like Tymoshenko) because they basically had him under their thumbs, and they preferred him to any real pro-Russian leader because they didn't want to be forced into the Eurasian Customs Union, which would deprive them of the money they could make from the far wealthier West.
So Yanukovitch basically bankrolled a propaganda campaign in favour of European integration which only began succeeding recently. He (and his backers) figured that this would work well for all involved; the Western Ukrainians that dislike Yanukovitch tended to be in favour of EU integration anyway, the oligarchs would get their European market access, and the Eastern Ukrainians, well, while they would be basically screwed over, it's not like they'd have anyone else to turn to. Obviously Yanukovitch was very much in favour of European integration originally. But then something went wrong.
Specifically, the Europeans weren't so keen on Yanukovitch, since he wasn't a reliable pro-Western leader. So instead of sending a deal he expected, they sent a basically unacceptable deal that required Ukrainian industry comply with EU regulations, including any regulations passed in the future. Free trade with Europe in of itself would be damaging to Ukrainian industry in the near term, but the Donbass oligarchs figured that they would still be able to benefit overall. However, with the regulations included, Ukrainian industry would be utterly incapable of competing with the highly developed Western industries in place and would be utterly destroyed, to the benefit of absolutely no one. Obviously Yanukovitch couldn't accept this deal, but unfortunately for him he had propagandized so hard in favour of integration that turning against it led to outrage. At this point, he was doomed; he could accept the deal after all, but it would wreck the Ukrainian economy enough to turn even the integrationists at Lviv against the EU (and, by extension, him), and his oligarch friends would be ruined too. He could join the Customs Union, but the Donbass oligarchs would lose access to their European markets entirely, which was basically unacceptable. So he was forced to wait things out, sandwiched between Putin (who would have been okay with Yanukovitch as a puppet, but not as a puppet of largely anti-Russian oligarchs) and the EU (who were waiting for a more reliably liberal leader to take over to control), without the support needed to stay in power. That's basically why there weren't very many anti-Maidan protests in the East, as Yanukovitch wasn't even remotely pro-Russian.
Of course, now that Yanukovitch is gone, the pro-Russian Ukrainians have some options available, and obviously they don't favour EU integration in the slightest. So even discounting Putin's intervention in the short run, in the long run separatist sentiment is sure to run strong as the effects of integration make themselves known.