You may be trying to play data files (mp3) in an ordinary CD player and that won't work
In order for your music to play in a player that doesn't have the mp3 option you first have to convert the mp3 files into ordinary .CDA files which is the format used on ordinary CD's. Have you tried playing the CD in your computer using Windows Media player? If it works there and not on a CD player it probably means you have burned mp3 files onto the CD and those will definitely not work in an ordinary CD player. I hope this clears things up a bit for you.