Only the European Parliament doesn't take the real decisions.

There's the EC and bureaucratic ad-hoc groups that nobody appointed like the Eurogroup (an informal assembly of eurozone fin-mins with super powers that's not legitimized anywhere officially), the council of the EU (composed by state leaders and making decisions where strong countries like Germany and France have disproportionate influence using lackey satellite countries or debtors they control), etc.

Here's another Wikipedia link for you:

https://en.wikipedia.org/wiki/Democratic_deficit_in_the_Euro...