Here's what a few say about cleaning the mat piece. A good idea for future use is to put a waterproof cover over the mat part.
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I must agree with @jacesterlingsmommy, I use dish soap and warm water in the tub

Oh yea idk about that i want to say put it in the bath tub too but id hate of it would dissolve in the tub maybe some detergent on a rag and just spot clean it

@mommysweigart, it's more the bottom piece that has the wood or what ever than is in it. She threw up almost a whole 8 oz bottle

I've read making a solution and putting it in the bathtub to soak.

I read if you put the whole pack and play in the tub with hot water and mild detergent like dawn or you dish soap and let it sit for an hour drain the water then rinse and sit out side to dry then it should be good