Did you make an Audio CD, or did you just burn the music as files on a disc? Many modern players can handle mp3 files simply burned as data files, but some cannot.
There are many, many different methods and tools for making Audio CD's. What did you use?
One method I have used in the past is to make a cue file from the assorted music files using ImgBurn. Then burn to a CD using the cue file as input into ImgBurn.
And lastly, some players are just picky about burned discs. I would advise burning at 16x speed and use high quality CD's. Taiyo Yuden are the best, but are soon to be discontinued. They should still be available at most online shops right now, like Amazon, Rima and Supermediastore.