water damage to floor - please help!!

Hi I was hoping someone can help with this problem.

I am a renter and have just discovered that the wood under the vinyl tiles in the bathroom has water damage and is rotting. There has been a leak from the sink that I had put a bucket under but it obviously didnt catch all the leaks. My kids also splash water when they are in the bath and that has added to the problem.

Who is liable for this damage? I feel really bad because I should have reported the leaking sink much earlier. However I dont think it is completely our fault because vinyl tiles in the bathroom are ridiculous as they are not waterproof.

What should we do? It is really stressing me out. I feel worse than if this was my own house, I really did not want to cause any damage to their property.
Your obligation as a tenant is to report damage as soon as you notice it.

Therefore, immediately notify the agent that you are aware of damage to the floor. As the floor had vinyl tiles, you cannot be expected to lift tiles to inspect the floor. As the floor is rotting I expect the problem has been going on for some years. The owner is lucky you have found the rot.
builders bog

It is amazing what can be fixed with builder's bog for rotten wood.
Also the advances in under floor membranes for tiling can water proof a floor. You just pour the liquid goo onto the floor and level it off with a trough and wait 6 to 8 hrs for it to set and then put the tiles down.