We perform charge self-consistent density functional theory combined with dynamical mean field theory calculations to study correlation effects on the Fermi surfaces of the iron pnictide superconductors LaFePO and LiFeP. We find a distinctive change in the topology of the Fermi surface in both compounds where a hole pocket with Fe d(z(2)) orbital character changes its geometry from a closed shape in the local-density approximation to an open shape upon inclusion of correlations. The opening of the pocket occurs in the vicinity of the Γ (Z) point in LaFePO (LiFeP). We discuss the relevance of these findings for the low superconducting transition temperature and the nodal gap observed in these materials.