The first thing a new government done after kicking out Yanukovich was to organise a democratic elections for a new president
That does not fix the constitutional problem. Poroshenko may claim some legitimacy because he won election by a high margin, but the constitution itself is now viewed as illegitimate by a lot of people. Poroshenko is the legitimate president of an entity that is not Ukraine as we knew it.
It would have been easy to fix that, by just crafting a new constitution and having it approved by the People of Ukraine. I still do not understand why it was not done.