Why does pressure in a streamline flow decrease as the streamlines clump together?

Acc to Bernoulli's equation and theorm, the velocities of the particles in a streamline flow should increase as they clump together (and thus leading to decrease in area). I agree.. But why does the pressure decrease? Using P=F/A , shouldn't it be more like the pressure increases with decrease in the area? What does the term pressure of a streamline exactly refer to? Its more of a paradox to me!! Please help!