Confined at the nanoscale level, polymers crystallize much slower than in bulk, and in some cases, the formation of ordered structure results are inhibited within extremely long experimental time scales. Here, we report on the thickness dependence of the conversion of the amorphous fraction of ultrathin films of poly(ethylene terephthalate) during isothermal cold crystallization. We present a new analytical method assessing the impact of irreversible chain adsorption and permitting to disentangle finite size and interfacial effects. From the μm range down to a few tens of nm, we observed an increase in crystallization time scaling with the inverse of the film thickness, which is a fingerprint of finite size effects. Films thinner than ~20 nm did not crystallize, even after prolonged annealing in the temperature range where the crystallization rate reaches its maximum value. Noticing that this threshold corresponds to the total thickness of the layer irreversibly adsorbed within our investigation time, we explain these findings considering that chain adsorption increases the entropic barrier required for the formation of crystalline structures.