I think this is a bit unfair. The EU is a combination of the member states and institutions: the European Commission, the European Parliament, the European Council and the Council of the European Union. These bodies are made up of either people elected directly by EU citizens or by politicians from EU member countries, not dissimilar to how the federal government in the US is made up of either people elected directly by US citizens or by politicians from US member states.
And just as it would be unfair to describe the US as only its member states, I believe it is unfair to describe the EU as only its member countries.
The EU at its very core is international contracts between member states. All that the EU is is contracts between states. Thus, the EU itself is nothing but the member states acting from their sovereignty.