Washing Machine Problems - I feel dumb

Hello! I just bought a house where the previous owners had their washing machine hooked up in their utility room. The only drain we can find is a floor drain that has no pipes sticking out of it and a round grate (about 5 inches?) that is cemented in the floor. It has a little tiny hole punched into it so we tried just sticking the washers drain pipe thingy into it but water backs up and goes everywhere. Any ideas? Please!?!

Could there be a drain in the wall as part of the supply/shutoff assembly?

Washing machine problems

I have looked around the area where the supply comes from and do not see any kind of wall drain. Any other ideas?

Is there a utility sink? I've seen washers that drained into them. If there was a washer in the basement, it had to drain into a standpipe. To my knowledge, a washer just can't drain otherwise.