Look at the label on the battery you disassembled, if it says it's an Alkaline battery, you will not find manganese dioxide anywhere inside it. And wash your hands, before the alkaline component you've discovered burns you.
The old trick of getting manganese dioxide from batteries was best applied to a very old style, more common when I was young, not nowadays. FWIW, if you want manganese dioxide, a good source is a 9 volt battery. it contains 6 little 1.5V dry cells, stacked one above the other.