We present extensively Monte-Carlo simulations of two conically-shaped proteins in parallel and antiparallel relative orientation, embedded in a flat lipid bilayer membrane with zero bending elasticity. We found two protein attractive regimes. The first one, in the range r(s) < sigma(L), where sigma(L) is the lipid diameter and r(s) the distance between the surfaces of the two proteins, is due to depletion effects. The second one, in the range 1 < r(s)/sigma(L) < 6, originates from the density and orientational fluctuations of the lipids around each protein. It is found that the attractive force decays exponentially with a correlation length xi/sigma(L) approximate to 3.2 independent of the shape and the size of the proteins.