Supported clusters of transition metal atoms are key components of heterogeneous catalysts. Understanding their interaction with small molecular species is therefore an important step in catalyst design. In this work, we provide a detailed first-principles investigation of the adsorption properties of CO and CO2 on Pt-n (n = 1, 2) clusters supported by a gamma-Al2O3 (1 0 0) substrate. In particular, important parameters such as the stability of the Pt clusters, molecular adsorption energies and vibration frequencies were investigated. All Pt-2 clusters exhibit lower adsorption energies than their monoatomic counterparts, especially single Pt atoms embedded in the surface of the support. Atomically preadsorbed Pt acts as an anchor for the CO molecule, increasing its adsorption energy compared to the bare surface. The support actively participates in stabilizing the adsorbates and a markedly different behaviour can be expected depending on the adsorption site being on the surface of small Pt clusters or on the Pt/support interface. Vibrational frequencies of CO and CO2 adsorbed on the supported clusters can be used to gain insight into the degree of dispersion of the metallic component of the catalyst, and can be profitably used in the design of novel single-atom catalysts (SACs).