A meteor (the word for a rock that has entered the earth's atmosphere and has yet to reach the ground) travels at an enormous speed and with a lot of energy. Once the meteor strikes, it is now a meteorite. Since the Earth's surface is a lot denser than the air through which the meteor was travelling, the energy that the meteor has as kinetic energy (i.e. its speed and mass), now has to be converted into other forms of energy as the ground will resist its movement (conservation of energy). This therefore results in a lot of heat, shock-waves and that kinetic energy transferring to the earth's surface and the meteorite itself, resulting in it being broken up into many small pieces.
We do often find meteorite's after the impact, it is in fact one of the primary ways we have determined the composition of elements in our solar system during the time of the Earth's formation. However, between chunks of the meteor vaporising and breaking up as it travelled in the atmosphere and the immense amount of energy released when the meteor strikes the surface, it breaks apart even further and is harder to find.
Lastly, the shape of the crater doesn't necessarily mean there should be a bit of meteor left in its centre. The shock-wave created from the impact is what creates the crater not the actual rock itself. A small difference but an important one.