That's one of the things I like most about the EU, its strong laws in favor of citizens (privacy, health, etc).
Whilst these are great ideas, this is not really democracy. I think it's also the source of much anti EU sentiment. I wish more of this stuff would be decided in public debates. I wish elections had more of an effect on the EU.
At the moment it feels like policy is being made by academics and beurocrats. And whilst it is good policy, it still feels wrong. I am afraid we are keeping it this way because we think otherwise we would have shite policy.
Literally every single part of the EU apparatus is democratic. Every single bit.
The European Council consists of the Heads of Government of the EU states. If your Head of Government isn't democratically elected then you're already fucked and the EU isn't making anything worse.
The European Commission is chosen by the European Council, so derives its mandate from that.
The European Parliament is literally elected.
The Council of the European Union is basically 'all the agricultural ministers' or 'all the finance ministers' or 'all the defence ministers' etc. Obviously these people all have democratic mandates in their home countries, thus the body as a whole has a democratic mandate.
By no means in any way is there any possible justification for describing the EU has undemocratic. It's actually much MORE democratic than many of its members.