Various intermetallic compounds harbor subtle electronic correlation effects. To elucidate this fact for the Fe-Al system, we perform a realistic many-body investigation based on a combination of density functional theory with dynamical mean-field theory in a charge self-consistent manner. A better characterization and understanding of the phase stability of bcc-based D0(3)-Fe3Al through an improved description of the correlated charge density and the magnetic energy is achieved. Upon replacement of one Fe sublattice with V, the Heusler compound Fe2VAl is realized, known to display bad-metal behavior and increased specific heat. Here we document a charge-gap opening at low temperatures in line with previous experimental work. The gap structure does not match conventional band theory and is reminiscent of (pseudo) gap characteristics in correlated oxides.