The EU is democratic: it empowers the democratically-elected governments of 27 states to collectively make policy (most of the time by unanimous voting, traditionally), and then empowers the population at large, as directly represented in EuroParliament through proportional methods, to amend or reject such policy.

The Commission is not instated by God Almighty or by hereditary laws: it is nominated by democratically-elected national governments. The Council does not spring fully-formed from the head of Zeus: it is made of democratically-elected governments. The European Court of Justice was not created by the Pope 1000 years ago: it was created by democratically-elected governments through treaties. And so on and so forth.

The fact that such governments are then able to sustain the fiction that they have no say in EU matters, is more a reflection of the poor state of critical thinking in voters across the continent than an indictment of EU's "democracy level", whatever that might mean... unless we assume that a process is democratic when it agrees with one's opinions, and completely tyrannical when it doesn't.