After my computer shuts down, I still have the power to the keyboard and mouse. This causes both the keyboard and mouse to have lights that remain lit while the system is off. How do I change this, so when I shutdown these also turn off?
This is normal with some motherboards. It's due to the +5v AUX being active. Some motherboard have jumper that can turn it off. You can also check your BIOS to see if you are able to disable a setting that allow your system to be awake via keyboard or mouse signal.
Your best bet is to read the motherboard's Owners Manual to find a solution on exactly how to disable it for your motherboard.
Instructions to Disable +5V-Standby for ASRock N68-VS3 FX
Source: This was taken directly out of the manual for the ASRock N68-VS3 FX motherboard