Bernoulli's principle is applicable to an inviscid, incompressible fluid at steady state with gravity as the only body force. Now look at the equation closely,
P/rho+V^2/2+gZ=constant
The first term is pressure energy or flow energy (energy required to push the neighbouring layers of fluid so that the flow continues) per unit mass. The 2nd term is kinetic energy per unit mass. The 3rd term is potential energy per unit mass.
The sum of all these 3 gives the total mechanical energy per unit mass, which is constant. In case if a nozzle the kinetic energy increases and to compensete that pressure or flow enrgy reduces. This results in decrease in pressure.
Bernoulli's equation is nothing but conservation of total mechanical energy for the above mentioned fluid. So just for the sake of the conservation pressure reduces.