The parasitic drag losses incurred by wet clutches, used in transmission systems, can significantly affect vehicular powertrain efficiency. This paper presents a novel implicit solution for hydrodynamic parasitic drag losses of disengaged clutches. These are generated by conjunctional friction, taking into account lubricant film separation during co-directional and counter-directional disc pair rotations. Lubricant film rupture is considered through application of incipient reverse flow boundary condition, which is representative of lubricant film separation. The results point to the operating conditions at which significant power losses occur. In particular, the time efficient model is able to represent the small losses incurred during co-directional rotation of disc pairs.