The trainer planes will want to float and "keep flying" when slowing down as that's how the wings are designed. In windy conditions you will notice it even more. As stated, try lowering the throttle more quickly as you line up and come into your approach. Let the plane settle in as the speed bleeds off and it will start to drop slowly as the wing wants to keep it in the air.  If you throttle back too soon the plane will land short as you experienced and if you do it too late the plane will overshoot the runway as you experienced.
The "trick" is to lower the throttle sooner rather than later and if the plane starts to settle to short of the runway then gently add in a little power to bring you further ahead and lower the throttle again and let it settle in again then as the wheels get close gently pull back on the elevator to bring the nose up slightly and let it down on the mains.
After enough times you will know how each plane reacts in calm and wind and you will know how to handle the throttle for landings.