The ablation by ultrashort laser pulses at relatively low fluences i.e., in the thermal regime of solids wetted by a thin liquid film is studied using a generic numerical model. In comparison with dry targets, the liquid is found to significantly affect ablation by confining the solid and slowing down the expansion of the laser-heated material. These factors affect the relative efficiency of the various ablation mechanisms, leading, in particular, to the complete inhibition of phase explosion at lower fluences, a reduced ablation yield, and significant changes in the composition of the plume. As a consequence, at fluences above the ablation threshold, the size of the ejected nanoclusters is lower in presence of the liquid. Our results provide a qualitative understanding of the effect of wetting layers on the ablation process.