Siannah: But as far as I'm aware, there was no threats towards Crimea, easter Ukraine or the pro-russian side of the country and therefor absolutely no justification to send a military force in.
Phasmid: There
was also talk of "punishing" separatist sentiment from the interim President just after the take over, to whit: "Anyone held responsible for separatist moves should be punished, his press service quoted Mr Turchynov as saying in a later statement, Reuters news agency reports."
Separatistic moves or facing a political opposing government, is hardly on the same page. If the roles would have been switched, I'm rather sure Mr. Yanukovych would have warned about separatistic sentiments, too.
I'm not gonna claim the "new" government did all the right things. Someone calling to ban the opposing political parties isn't a "strong indication", certainly not stronger then Yanukovych claiming the people on Maidan as terrorists or foreign forces - if that's justification to send troops into another country, we'd see this happen at least 20 times per year all over the world.
If Russia would have send additional troops just into their base in Sevastopol, everyone could justify and understand that - even the Ukrainians would had to accept it, even though teeth-gnashingly. But moving onto foreign soil, is quite another step.