All naturally found and technologically fabricated solid microparticles possess surface roughness. Upon optical wave scattering from such particles, in addition to its geometric shape, the surface relief becomes an important morphological factor determining the optical properties of the scatterer. We present results of the numerical 3D-simulations of focusing an optical wave with a dielectric microsphere with randomly distributed surface roughness. We address different cases of azimuthally symmetric and asymmetric distortions of the particle surface. We show that the key parameters of the near-field focal region (intensity, longitudinal and transverse dimensions) referred to as a photonic nanojet (PNJ) are sensitive to changes in the microsphere surface texture. Two important PNJ parameters, the peak intensity and the longitudinal length, are subject to more prominent changes. The influence of the optical contrast (relative refractive index) of the microsphere on PNJ parameters is investigated in detail. The possibility of reducing the influence of surface roughness on the near-field focusing strength by microsphere watering (water-uptake) is demonstrated.