You need to convert the files from mp3 format to "audio" format.
"audio" format is the format used on proper music CDs.
I have Nero for example, and when it starts up it says do you want to create a DATA CD or an AUDIO CD.
If I chose DATA it puts the mp3 files on the CD as "data", and while some players can play them many cannot.
However if I select "Audio" it converts the mp3 files into Audio format and makes them into an Audio CD.
Windows Media Player can also burn files in audio format, although the wording may be different, it may not say "data" and "audio" but something else.
Note you can get FAR more mp3 files on a CD than Audio files so you need to select about 70 minutes worth of mp3 files to make an audio CD.