If you want to take your cleaning even further, combine equal parts warm water and vinegar, dampen a washcloth with the mixture, and wipe each slat. (Just be sure not to use this on wooden blinds!)
Sprinkle a generous amount of baking soda onto the stain (enough to cover it completely) and allow it to sit for one to two hours. After time is up, thoroughly vacuum up the baking soda to reveal clean, dry fabric.