A solid-state dye laser with a microcavity whose size is comparable to the lasing wavelength is modeled by means of the finite element method. The position of the pumping source affects the lasing mode spectrum. In comparison with a single point source at the edge of the cavity, a random distribution of excitation sources in the central gain part of the microcavity leads to depletion of odd longitudinal modes and to higher output efficiency of the laser radiation in even modes. The simulation results are explained by simple physical considerations.