Motivation: The standard approach for statistical inference in differential expression (DE) analyses is to control the False Discovery Rate (FDR). However, controlling the FDR does not in fact imply that the proportion of false discoveries is upper bounded. Moreover, no statistical guarantee can be given on subsets of genes selected by FDR thresholding. These known limitations are overcome by post hoc inference, which provides guarantees of the number of proportion of false discoveries among arbitrary gene selections. However, post hoc inference methods are not yet widely used for DE studies. Results: In this paper, we demonstrate the relevance and illustrate the performance of adaptive interpolation-based post hoc methods for DE studies. First, we formalize the use of permutation-based methods to obtain sharp confidence bounds that are adaptive to the dependence between genes. Then, we introduce a generic linear time algorithm for computing post hoc bounds, making these bounds applicable to large-scale DE studies. The use of the resulting Adaptive Simes bound is illustrated on a RNA sequencing study. Comprehensive numerical experiments based on real microarray and RNA sequencing data demonstrate the statistical performance of the method.