Most mice and keyboards enter a "sleep" of their own after some inactivity, and require exaggerated use to wake up.
The wireless mouse on my retina will NOT wake up for movement, you have to click a button. So if the computer is screensaver and I bump the mouse, it won't usually wake up. Gotta click the mouse in the morning.
If your peripheral isn't doing that, your only recourse may be to replace it.
On a side-note, I've also seen other random peripherals keep computers awake... controllers, printers, scanners, and the like. Get an all-in-one unit and try to use its "copy" function to make a copy of a paper, and doing so wakes up the computer, despite not involving the computer at all. Or printers that when attached and powered on completely prevent computer sleep.
I work for the Department of Redundancy Department