Could be wrong here but if I get what you're after your backup should be hopefully setup as a maintaince task/SQL Agent Job.

If you right click on the task itself and select "View History" it will give you the information you require i.e. Date, Plan Name,Duration, Error Number & Error Message (plus more). You can then investigate that error message in full.

Hopefully that's what you were trying to get as an answer - if not expand more.