In the article where I found the demands of Sinn Fein the author Sinn Fein MEP Mary Lou McDonald also wrote (emphasis mine)

We argued that the Lisbon Treaty would deepen the democratic deficit by removing Ireland's permanent commissioner, reducing our voting strength at council, removing or weakening key strategic vetoes, such as on taxation and international trade, and by giving the European Council the power to amend the fundamental laws of the union.

So "democracy" here means veto rights, and a council voting system which is completly unproportional to the population of a country.