Nope..you are supposed to bleed after taking the pill.  The purpose is to drastically increase your hormone levels and then have it drop- which will trigger the shedding of the uterine lining- its called a withdrawl bleed. Without a uterine lining there isn't anything for a potential embryo to attach to.

You also aren't late for your period... the bleed you were talking about was the beginning of a new cycle so you count from the first day of full red flow...