EU policymakers recognize the importance of preserving a highly integrated European economy. They are, however, making the same mistake that led to the euro mess in the first place: pretending that Europe can be integrated through administrative measures alone. Remember that the euro was adopted despite worries that the fiscal and political differences across the eurozone would be too large to make it what economists call an optimal currency area. Those differences are still being overlooked. In a recent speech at Jackson Hole by Jean-Claude Trichet, the former head of the European Central Bank, declared that the EU was like the U.S. minus a fiscal union.

Well, perhaps not. Short-term measures to fix or contain the present financial mess are indeed necessary, but in the long run Europeans must change culturally and politically if they are to achieve the balanced integration needed to make the euro a success. This is more crucial than ever because recent setbacks have weakened the case for integration in many people’s minds.

Gains can be achieved by promoting trade among European nations and, more broadly, by increasing trust among the Continent’s citizens.

Geographically, most modes of transport still cost much more within the EU than in the U.S., a factor that hampers trade. EU leaders need to overcome preferences shown to national champions and find better ways to coordinate Europe’s transport, communications, and energy infrastructure across national borders.

Economically, the discrepancy in productivity, and thus average income, is much greater across European nations than across U.S. states. Despite these differences, labor migration rates are much lower in Europe.

Culturally, surveys suggest that almost half of Europeans trust citizens of their own country “a lot,” but only 20% express the same level of faith in Europeans from other countries. This distrust manifests itself in such episodes as Germans leaping to blame Spanish farmers for selling them killer cucumbers, even though the problem originated at home. And this trait has been exacerbated by the recent financial mess.

While cultural change is bound to be challenging, much can be done. Research shows that higher education generally reduces suspicion of outsiders. Of course, education that highlights European interdependence might have an even more powerful effect. The Erasmus educational exchange program for students has already built significant bridges across Europe and — even at a time of budgetary stringency — is worth expanding. Participation in regional economic networks is another idea deserving more attention as technology enables richer communication and broader reach.

While none of this is guaranteed to work, there is no alternative to trying. Because without such integration, Europe will amount to a lot less.

–Pankaj Ghemawat, a professor at IESE Business School in Barcelona, is author of World 3.0 (Harvard Business, 2011).

This article is from the December 26, 2011 issue of Fortune.