Probably the greatest impact is your shutter speed of 1/60th second. Even though you're panning, the car is moving fast.
Boost your shutter speed to it's max (at least 1/1000th). In addition, use a tripod or at least a monopod. Brace yourself while panning, as best you can.
A 300mm lens brings the action in close, but will likely cause vibration, ESPECIALLY if it's not an image-stabilized lens. The heavier the lens, the more likely is camera shake.
Not sure why you used 1600 as ISO, but since camera model not mentioned, it may be causing some grainyness too.
You might experiment with pre-focusing on a spot on the track as zoom OUT a bit and then crop the final results. You also didn't mention if you used auto or manual focus. Either one could have contributed a bit to the blur, depending on camera model and lens quality.
