Practice is not the simple answer. The right kind of practice is needed ...
There are two sides to the brain. We habitually switch from one side of the brain to the other when we do certain things, and we are not conscious that we are doing it.
When you vocalise in any way (talking,singing) you use one side of your brain to prepare the vocalisation, then switch to the other side to use the speech centre to give a vocal output.
When you play an instrument, you use only one side of your brain - the same side that you use to prepare the vocalisation - UNLESS you look at the instrument to see what you are doing. When you look, you engage the other side of the brain again.
If your brain is switching sides while switching tasks, it gets confused - that's when it gets hard to do two things at once. So before you can feel comfortable singing while you play, you have to practice playing without looking at your fingers.
Stare out of the window, practice when watching TV with the sound off, just make a point of not looking at your fingers when playing - you will be surprised at how often you are doing it, when you are trying to avoid looking.
When you can play the tune without looking, you will find it much simpler to sing while playing - in fact, it should be no trouble at all!
Incidentally, the same skills are involved in learning to touch type - you might try to learn touch typing, it really does improve your guitar playing (again, as long as you resist the temptation to watch your fingers).
