One thing that helps me prevent this during brewing--since once the wort goes into the fermenter I am toast and don't want to bother cleaning anything--is to clean as I go along. Once the boil gets going I clean and rinse my MLT, while waiting for my alarm to tell me to pitch the next hops addition. This is easy because I don't have to leave the brewing area, since I brew in my garage with the door open, I'm never very far away, and never out of earshot. At each step, while waiting for something to finish (mashing, boiling, aerating, etc.) I clean whatever was used in the last step and prep whatever will be used in the next step. With the way I stack my brew day, after my fermenter goes into the closet all I have left to do is clean my air stone, air hose, a single funnel and my starter jar. I often leave the last bucket of Star San with a lid on it to use for occasional sanitizing through the fermentation process--beer thief, fresh airlock, etc. This bucket is often the start of my bottling procedure.
"So you say you just brewed your first batch of beer. Welcome to the obsession." --me, to every first time brewer I ever meet.