The European Commission is one of the most undemocratic institutions. These people [the EU commissioners] were not elected by anyone and they are not accountable to EU citizens.
The European Commission is the EU's executive arm. Commissioners are first appointed by EU member states and then, as candidates, take part in hearings in the European Parliament. The EP members - which are elected by EU citizens directly - can reject a candidate and had exercised this power in the past. As for the President of the European Commission, his candidacy needs to be agreed by the European Council - that is, by democratically elected leaders of every member state. The European Commission as a whole is subject to a vote of consent by the Parliament and are then appointed by the European Council, acting by a qualified majority.
In the whole process of appointing new EU leaders the results of the European elections have to be taken into account. See here for more information.
Article 5 of the Treaty on the European Union ensured the principle of subsidiarity, which guarantees that decisions are taken as closely as possible to the citizen and that constant checks are made to verify that action at EU level is justified in light of the possibilities available at national, regional or local level. It is the principle whereby the EU does not take action (except in the areas that fall within its exclusive competence), unless it is more effective than action taken at national, regional or local level.