The US stayed out of Moldova and Georgia. It didn't prevent them from seeing Russian troops. I doubt Ukraine would have been different.
The problem was the three way race that put the pro-Russian Yanukovych in power. More people voted for his opponents, but since the vote was split between two other people, Yanukovych got a plurality of the votes. Yanukovych turned towards Russia, the population and parliament turned against Yanukovych, Yanukovych fled to Russia, it looked like Ukraine would turn back towards the EU, and then aided the rebellion with equipment and troops, and annexed Crimea in violation of their treaty with Ukraine.
I'd like to think Russia isn't pulling their foreign policy out of their behinds and they have some master plan, but the evidence doesn't support that view. Russia's feeding its own people BS, but the sanctions and dropping oil prices are hitting Russia hard. That doesn't bode well for long-term stability. And with Putin's attacks against the monetary oligarchs, he will likely end up forcing a showdown he was trying to prevent.