Effect of the asymmetry of the redox molecule (RM) coupling to the working electrodes on the Coulomb blockade and the operation of molecular transistor is considered under ambient conditions for the case of the non-adiabatic tunneling through the electrochemical contact having a one-level RM. The expressions for the tunnel current, the positions of the peaks of the tunnel current/overpotential dependencies, and their full widths at the half maximum are obtained for arbitrary values of the parameter d describing the coupling asymmetry of the tunneling contact and the effect of d on the different characteristics of the tunneling contact is studied. The tunnel current/overpotential and the differential conductance/bias voltage dependencies are calculated and interpreted. In particular, it is shown that the effect of the Coulomb blockade on the tunnel current and the differential conductance has a number of new features in the case of the large coupling asymmetry. It is also shown that, for rather large values of the solvent reorganization energy, the coupling asymmetry enhanced strongly amplification and rectification of the tunnel current in the most of the regions of the parameter space specifying the tunneling contact. The regions of the parameter space where both strong amplification and strong rectification take place are also revealed. The obtained results allow us to prove the possibility of the realization of the effective electrochemical transistor based on the one-level RM.