Tying European countries together to form a single currency was always going to be difficult. Productivity is different in each country. And deeper than that, attitudes, lifestyles, and cultures are different.
This is probably the reason why productivity levels across Europe have not converged. In the past decade productivity in Germany grew by 9.4%, while in Italy it hardly changed.
Productivity at this level is GDP/head, so the Germans must have: worked harder or longer; reduced waste; invested in better technology; and/or developed new products/ services that commanded higher prices/profit margins.
Different areas within a region will always grow at different rates and responding to that requires more than just a central bank and shared fiscal policy. Both the US and European governments funnel money into needier areas. But Americans also move house more easily than Europeans to match changes in economic growth. Europeans are less willing to do that, and the corollary is that then wages must vary by location, to match the levels of productivity that people generate in different parts of the continent. For now, that means that wages must fall in Greece, Ireland, Italy.