If you play a piece of simple familiar music that you already know and hum along while your playing, that will help you get used to what a count should be. Practice it till you are able to play it exactly as you hear it in your head. Also, playing along with a CD helps you develop your counting. If you can't keep up with the CD then just use your right hand in the beginning.
Actually, I have an adult student that concentrated so hard on getting the counting right that she never could play the song at the right tempo, even though she knew exactly what the music should sound like. It was difficult to get her to stop counting. I personally don't think it is THAT important when you are a beginner, like you said, it's too much to concentrate on. Play the music, it might be a little slow, the counting may be a little off, but it will correct itself later on.