So you took the controller apart, pulled the stick off the thing its connected to and replaced it?
Its hard to explain since I dont know the name of what the thumb stick is connected to...
That is what the thumbstick is connected to, and when you move your thumbstick, the piece of plastic sticking up will move with it, Then that box senses when the thumbstick moves etc...
I have not taken it apart, nor do I know if you can but, I assume inside there are some springs, or something under tension, so when you take your finger off the thumbstick it will return to the centre. Sounds to me like you have broken this... or if it is springs, they may have come loose.