Ironically, there is also a democratic deficit in the UK. The House of Lords is not elected at all, and the district system ensures that minority opinions do not get represented in the House of Commons. As a result, UKIP is far bigger in the Europarliament than in the House of Commons.
Yes, there was a democratic deficit in the original EU structure. It was addressed in the 2009 treaty, and it keeps getting addressed with more and more decision-making powers slowly moving from Commission to Parliament. But it's too late, people think Bruxelles decides banana sizes and we can't have that.
Unsurprisingly, who was among the first journalists starting the whole "crazy bruxelles" meme? One Boris Johnson.