Where and how deep was the cut?
If it was just torn a little, that's actually really normal to happen during sex. Little tears can happen inside the vagina from rough sex or from fingernails or other things.
I guess if you're really worried about it getting infected, and it's outside, not inside your body, you can wash it up with some antibacterial soap and cover it.
If it's inside, I wouldn't worry. I mean, if you cut the inside of your mouth, you just let it heal, right? You don't worry about your mouth getting infected... and your mouth is dirty dirty!!!