Earlier quoted context omitted.
That's precisely the thing. Whenever EU does something people don't like, they hate EU, not the council members who voted for it.
Because it is exactly the EU governance that lacks democratic representation, enabling unfavoured politicians to remain in significant power. You can only elect MEPs (via party lists) locally. The majority of legalislation is drafted by the technocratic European Commission and legislation is mostly passed through parlaiment unchanged from there. There are many nationally disgraced politicians seating in the EP, EC or…
So, even if they might not be explicitly elected to be in the EU governance, most of them have reached that spot through more or less democratic means. "More or less" because Prime Ministers are usually nominated not elected, but that's still as part of each country's democratic process.