If at the time of performing salat, you honestly believed you were doing your best to perform your salat on time, then it will be accepted insha'Allah. There is a big difference between performing salat at the wrong time because of honest mistake and performing it at the wrong time due to convenience or laziness. You would not have to make it up (by my understanding, as limited as it may be) because you have already performed it, unless you performed the wrong salat at the wrong time, that would put you short of your five prayers a day, in which case you should make up the one you missed.