The following applies specifically to a Whirlpool LSQ9560PW2 washer purchased about 2005, but may apply also to yours. It is worth a look.

In the above model, the "little piece" is not little. It extends from the base of the timer up through the hollow knob-shaft to the top of that shaft where a little of it can be seen (in the photo from Gene) as the dark area between the prongs of that shaft, where it serves to lock those prongs apart, keeping the timer knob on.

In my case this piece was not well seated, and, after 5 years, worked its way out the bottom of the shaft and out of the bottom of the timer. To see if this is your situation, open the controls console (on the above model, two little screws seen from the top at the very back extreme left and right corners) and see if you can find this dark, long, thin piece - it may still be partially sticking out the bottom of the timer. If so, reinsert it home.