My mother used to tell be that I was always dizzy, so flying comes second nature!
Seriously, dizziness will go away with more practice. I agree with Brett that to fly a good pattern, you have to watch closely during the inverted laps, and actually during the entire pattern.
Unlike other events we get to stop turning during the maneuvers.
But never forget that the entire pattern is a presentation, meaning that you should concentrate also on the level laps between maneuvers. While it is true that the level laps are not scored, it is part of the package that will set up all your maneuvers. Concentration should not end until the airplane has stopped after the landing.