Hi,
have you considered offering your employer to work on a day you would normally be off (to catch up on your work)? That way you won't loose your day's pay and your employer will see you as a hard working team player. That's a win - win solution... :-)
I appreciate this might not be easily done if you work in an office which is only opened for business Mon - Fri. but in let's say retail, that would be a great solution.
Otherwise I would try to use one of my holiday days.
You can't expect an employer to "reward" people for not working. - That way most of people would pull a sickie every time they sneeze or have a little head ache after a night out!
And don't forget they probably had to pay somebody else to do the day's job for you.
Offer to work extra - it's only fair...
Good luck!