Using a generalized version of the Weyl-Riesz criterion for compactness of subsets of Lebesgue-Bochner spaces, we present in this short note an alternative proof of a result by J. Simon [4] that extends the classical result by J.P. Aubin and J.L. Lions on compact embeddings in Lebesgue-Bochner spaces to the non-reflexive Banach space case. © 2013 Springer Basel.