What you need is a product called flotex.
It is a short pile waterproof type of carpet used predominately in hospitals, nursing homes, kindergardens etc. Anywhere there could be spillage and needs hot water to clean it etc.
It has a synthetic rubber back and will let nothing through. comfy to crawl around on too.
Just hose it off to clean it as water has no effect on it.
And yes, I am in the trade.