This usually happens when one of the pieces is on on top of another piece and blends in with the puzzle. If this happens again just use the "shuffle" button located on the left side of the game. This will shuffle the pieces around and make it easier to find that last missing piece.
I used to take care of a Lynx at a rescue. He would sit on a shelf above my head as I worked in his enclosure and he would gently pet me on my head and purr sometimes.