I have "Media Center" (not to be confused with "Media Player") and use it only for watching DVDs.
Windows 8 does still have "Media Player" which I use in the same way as you -- to quickly audition a newly burned CD.
Go to the start menu. Right click and turn on "all apps".
Scroll over to "Windows Accessories" and you will see it: "Windows Media Player"
Go to your desktop: Settings/Control Panel/Default Programs/Change Auto Play Settings.
Scroll down to CDs/Audio CD/
and select from the pull down menu: "Play Audio CD (Windows Media Player)
Now when you put in an audio CD, "Media Player" will automatically start.