Why on Earth you even consider charging a flaky file system like exFAT with a critical task like storing back-up data? Lucky for you, you can't do it. Format your backup drive to HFS+ Journaled and get on with life.
You can generally backup to an HFS+ sparseimage that is on an exFAT drive if you have to. As MisterMe said, why would you want to? I've had some issues with exFAT drives myself.
Hy, I have the same problem, the reason for use the ExFat is because it can be used with Windows, I've got some files on my Mac and some other on a Pc.
Thank's in advance