In this work, the interactions of NO and CO molecules with silicon carbide (SiC) and germanium carbide (GeC) graphene-like nanosheets, functionalized with titanium and copper atoms, are comparatively studied through density-functional calculations. The results indicate that NO and CO molecules are only slightly adsorbed on the pristine carbide nanosheets. Also, the copper and titanium adatoms are chemisorbed on the monolayers, leading to stable functionalized carbide nanosheets. These adatoms greatly enhance the binding energies of CO and NO. In particular, the titanium-functionalized GeC monolayers display the highest adsorption energies for CO and NO and also the largest changes in their work functions upon molecule adsorption, indicating that they could be useful for trapping or detecting these molecules.