Several studies have suggested that introgressed Neandertal DNA was subjected to negative selection in modern humans. A striking observation in support of this is an apparent monotonic decline in Neandertal ancestry observed in modern humans in Europe over the past 45,000 years. Here, we show that this decline is an artifact likely caused by gene flow between modern human populations, which is not taken into account by statistics previously used to estimate Neandertal ancestry. When we apply a statistic that avoids assumptions about modern human demography by taking advantage of two high-coverage Neandertal genomes, we find no evidence for a change in Neandertal ancestry in Europe over the past 45,000 years. We use whole-genome simulations of selection and introgression to investigate a wide range of model parameters and find that negative selection is not expected to cause a significant long-term decline in genome-wide Neandertal ancestry. Nevertheless, these models recapitulate previously observed signals of selection against Neandertal alleles, in particular the depletion of Neandertal ancestry in conserved genomic regions. Surprisingly, we find that this depletion is strongest in regulatory and conserved noncoding regions and in the most conserved portion of protein-coding sequences.