In this work, we study the limitation of resource concentration by looking into the properties of resource measure. More specifically, we show the no-go theorem for concentration of a resource measure which satisfies the monotonicity and the so-called tensorization property. We first present our main result in the general framework of quantum resource theory, and then show applications for nonclassicality measures: the nonclassicality depth and the metrological power. We find the strict no-go theorem for nonclassicality concentration which states that the nonclassicality depth can never be concentrated by classical operations. On the other hand, the metrological power of nonclassicality can be concentrated probabilistically while it cannot be increased on average. We also study the nonclassicality depth of channels so that we find using entangled input states do not help to preserve the nonclassicality. This work leads us to understand which operations are required to obtain resourceful states.