How to make homemade dryer sheets?

I recently bought a new washing machine, without realizing that it doesn’t have a fabric softener dispenser.  I have a whole bottle of softener. Short of running to the basement, trying to catch the rinse cycle, is there any way that I can make my own dryer sheets?
 
(I tried one of the balls that you fill, but it didn’t release the softener.  I wonder if it has anything to do with the way the new machines are designed to save water.)
 
Any help would be appreciated.