Au/Co/Au nanopillars fabricated by colloidal lithography of continuous trilayers exhibit an enhanced coercive field and the appearance of an exchange bias field with respect to the continuous layers. This is attributed to the lateral oxidation of the Co interlayer that appears upon disk fabrication. The dependence of the exchange bias field on the Co nanodots size and on the oxidation degree is analyzed and its microscopic origin clarified by means of Monte Carlo simulations based on a model of a cylindrical dot with lateral core/shell structure.