When a tax is imposed on the sellers, the price of the good rises. So, why doesn't the demand curve shift? A tax imposed by the government on the sellers would drive up the price of the good. I understand that the supply curve will shift upwards due to this but the won't the demand curve also shift downwards due to the increase in price of the good?
I think you're confusing quantity demanded, and the demand curve.

The demand curve tells you how much quantity should be demanded at each price point. Therefore changes in price should change the quantity demanded, not shift the curve. You want to think of this in terms of demand and supply shocks.

For example: 

Imagine it was discovered that bananas gave you super powers. Now the ability to supply bananas hasn't changed (no supply shock), but the desirability of bananas at any given price point has increased (demand shock).

An increase in price due to taxation has not impacted the desirability of goods at any given price point. It simply changes the price point.