  The model developed for LaMnO$_3$ addresses the spin-orbital order by
superexchange and Jahn-Teller orbital interactions in the cubic (perovskite)
symmetry up to now whereas real crystal structure is strongly deformed. We
identify and explain three \textit{a priori} important physical effects arising
from tetragonal deformation: (i) the splitting of $e_g$ orbitals $\propto E_z$,
(ii) the directional renormalization of $d-p$ hybridization $t_{pd}$, and (iii)
the directional renormalization of charge excitation energies. Using the
example of LaMnO$_3$ crystal we evaluate their magnitude. It is found that the
major effects of deformation are enhanced amplitude of $x^2-y^2$ orbitals
induced in the orbital order by $E_z\simeq 300$ meV and anisotropic
$t_{pd}\simeq 2.0$ (2.35) eV along the $ab$ ($c$) cubic axis, in very good
agreement with the Harrison's law. We show that the tetragonal model analyzed
within mean field approximation provides a surprisingly consistent picture of
the ground state. Excellent agreement with the experimental data is obtained
simultaneously for: (i) $e_g$ orbital mixing angle, (ii)~spin exchange
constants, and (iii) the temperatures of spin and orbital phase transition.
