The pitch is wrong on the floor. You say that the floor is pitched towards the door, in actuality, your floor is pitched towards the front wall. Concrete guys can't seem to get it right when it comes to sloping away from corners. I specified to my concrete guy that if water pools in the corners he will be redoing the complete floor. He got that part right.
To help stop it, have your floor saw cut on each side of the door towards the back of the garage. This way when the water drips off of your car, it will be stopped by the saw crack. Other than that......keep a squeegee by the doors and squeegee out when the water gets too much.