You seem to be under the impression that the tail rotor pushes the aircraft forward. It does not. The sole reason for having a tail rotor is to counteract the torque reaction between the main rotor blades and the rest of the aircraft.
The tail rotor takes its driving force from the engines, so losing it actually causes an instant increase in engine rpm, because it is now doing less work. Unfortunately, you have lost the device which is stopping the aircraft spinning in the opposite direction to the main rotor blades. What the pilot must do - instantly - is reduce engine power dramatically, perhaps completely.
Isaac Newton had something to say on the subject.