It's very easy when listening to songs to ignore the music in the background, and only listen to the singers. One skill you really have to learn is the ability to "hear" the music in the back, try to focus in on some instruments like bass, strings, piano, etc. Try to find patterns and learn some of the little music tricks being employed. The more you develop this skill the more your own music will improve. Singers are great, but they only work well when they have a "skeleton" of good music holding them up.
Above are 2 pieces from the Christmas Medley to give an idea what the music sounds like, without any vocals, it certainly sounds different. You still sort of hear the singing, because the music is sort of suggesting it. Implying a melody is actually a good musical ploy.