Mercury chalcogenide nanocrystals generate a lot of interest as active materials for low cost infrared sensing. Device improvement requires building a deeper understanding of their electronic structure which combines inverted band ordering, quantum confinement and dependence to surface chemistry. This is particularly true with the development of mercury chalcogenide colloidal heterostructures (HgSe/HgTe, HgTe/CdS…). In this case the lattice mismatch induces a strain which affects significantly the band gap given the narrow band gap nature of the material. Here we study the effect of pressure on interband and intraband transitions in a series of HgTe and HgSe colloidal quantum dots. We demonstrate that in HgTe and HgSe, the nanocrystal morphology stabilizes the zinc blende phase up to 3 GPa. Under compressive strain, the interband signal blueshifts by 60 meV/GPa, while the intraband transition redshifts by a small amount (8 meV/GPa). Using an 8-band k•p formalism, we reveal that the interband shift has the same origin as the one observed for bulk material (change of effective mass, followed by band gap opening), while the intraband shift can be attributed to an increase of effective mass only.