The main reason for the generation of tsunamis is the deformation of the bottom of the ocean caused by an underwater earthquake. Usually, only the vertical bottom motion is taken into account while the horizontal co-seismic displacements are neglected in the absence of landslides. In the present study we propose a methodology based on the well-known Okada solution (Okada 1985, 1992) to reconstruct in more details all components of the bottom coseismic displacements. Then, the sea-bed motion is coupled with a three-dimensional Weakly Nonlinear (WN) water wave numerical solver (Dutykh et al. 2012) which allows us to simulate a tsunami wave generation. We pay special attention to the evolution of kinetic and potential energies of the resulting wave while the contribution of the horizontal displacements into wave energy balance is also quantified. Such contribution of horizontal displacements to the tsunami generation has not been discussed before, and it is different from the horizontal impulse of continental slopes faulting of Song et al. (2008) and the first-order contribution of the horizontal displacements of Tanioka and Satake (1996). Approaches proposed in this study are illustrated on the July 17, 2006 Java tsunami and some more recent events.