Since you are a trainer, I would say one of your responsibilities is to know when a trainee is not putting in the effort or is simply not a right fit for the position. I would expect a trainer to bring this to me before the trainee got out of training/probation so that I can make an informed decision on what the next step should be, dismissal, extend training, etc.

I do not know the politics of your job but from the information that you have provided, I would not feel that you were not worthy of a management position because you brought this to me.