They "lost their vote"? Yanukovych fled, that was his choice. It also ignores the donbas voters who voted for him because of the EU treaty. And they held elections after in which donbas votes counted the same as everyone else. Donbas also voted for Ukraine independence from the Soviet union in the 90s.
Putin demanded yanukovych cancel the EU treaty and instead sign a treaty with Russia. He threatened to stop selling Ukraine gas below market rate. This is the same way he controls lukashenko. Yanukovych went to the Europeans and begged them to make up what Ukraine would lose paying market rate but they refused. So he was forced to cancel the EU treaty which he didn't want to do because he knew what would happen. Rock and a hard place. He was corrupt but not stupid.
>Yanukovych stood for economic modernisation, greater economic ties with the EU, and military non-alignment.
>In November 2013, Yanukovych suddenly withdrew from signing an association agreement with the EU, amidst economic pressure from Russia.
From the Wikipedia.