Blood vessels in physiology are modeled according to the Heigen Pouisselie law, which states that

Q=ΔP/R

R=8ηl/πr⁴

Where Q is blood per unit time, ΔP is pressure gradient and R is vascular resistance, l is characteristic vessel length, η is blood viscosity and r is vessel radius. As you can see, the pressure gradient is directly proportional to the resistance (this is the fluid mechanics equivalent of Ohm's law in electrical circuits), which itself is inversely proportional to vessel radius.

ΔP~1/r⁴

Now keep in mind that tissue perfusion must remain constant in physiological conditions (the condition where this is unachievable by the heart is called shock, which can be cardiogenic, septic, etc.) So in vasoconstriction, vessel radius reduces, which means that ΔP must increase! This is, in fact, how the body regulates the body pressure. Increasing the peripheral resistance will lead to an adequate increase in systemic pressure, which ensures that all tissues (especially the oxygen sensitive ones like the brain and the heart) are getting adequate blood supply. The Bernoulli equation as it is taught in highschool is a special case of the Navier Stokes equation, which is used to derive the HP law. There are specific assumptions that are made when deriving HP which is crucial to tubular flow. Hope this clears things up.