I've heard this often and I don't understand it at all.
Every government in the world has a permanent set of employees which enact policy and turn political intentions into legislation. Usually these are split into departments, each headed by temporary political appointee.
So exactly like the European Commission, then. Why is it only "undemocratic" when the European Union does it?
Are you suggesting that all 32000 people working for it should be elected? I'm quite certain there is no government in the world which does that and it seems quite impractical.
Or should every political appointment be directly elected, instead of appointed by a head of state? You could do that, but I am not aware of any major government which does so, so if that's the sole reason to call it "undemocratic" then it's a double standard.