Most of us have been under the false impression that if you practice, practise, practice you get better. What if you are practicing wrong? Those are hard habits to break. It could be as simple as inflection, timing, an incorrect note or even breathing. As a vocal coach and singer, I believe that is it is worth it to take the time to learn how to practice correctly and save yourself a lot of time and work. "Work Smarter - Not Harder".
So how do you practice correctly? My suggestion is to work your song in small increments! Perhaps you sing your first verse but your timing is off in a phrase. Don't go onto the next part of the song until you get the phrase you are missing. Take it back to that exact place and find out what you are doing wrong, keep working it until you "nail" it! Then move on to the next. It is way simpler to learn a song when you know what is going on instead of making it up. That doesn't mean you can't put your own spin on it, it just means learn it first.
Sometimes you want to be able to do the vocal aerobics that professional singers do. Let me tell you it is a mistake to just jump into the run without knowing where you are going. That would be like racing down a rocky path blindfolded and realizing too late you have gone over the edge with no return. Break it down, learn the notes; know where to start and when to end, and what note to end on. If you don't know where you are going you won't know where you will end up and it can be nasty.
Practice is never perfect! That is why we do it. Expect to make mistakes because that is how you learn how to make it better. Sometimes those imperfections can lead to something even more beautiful. Allow yourself to grow! Don't focus on how bad it sounds, focus on how it is getting better, even if it takes time. Enjoy the process.