What sort of ticket do you have?
If it is an advance ticket (meaning that your ticket says 'Advance' somewhere on it - probably the top left hand corner) then the staff are right. If it's some other sort of ticket, then you can probably use it on the next train - whoever is the operator - although also see JCollins' point above.
It is probably worth finding the guard of the TPE train and asking them before boarding whether they will accept your ticket. They may be willing to help you
And please remember that us here are just people interested in the railways. Ultimately, in the circumstance you find yourself in, it's what the staff on the train say that goes.
Someone will be along soon with more detail, but this should get you going for the moment.