Go into your mouse settings as above and look for the feature called tapping and uncheck it. At least that's what my mouse (synaptics on a dell) calls it.

Tapping on the surface of the TouchPad is the same as clicking the left TouchPad "mouse" button. However, tapping is usually quicker and more convenient than using the mouse button.

It's irritating and drives me nuts. I'm glad you posted this, it reminded me I wanted to shut off the tapzones option too, that's been driving me nuts too.