You already have a good mathematical answer, so I will focus on an answer with almost no equations.
I take it you understand the basic mathematics of the simple harmonic oscillator.
When you add damping, the amount of energy you lose per cycle depends on the velocity: the faster you go, the more energy you lose (at the same amplitude) because the force scales with $k\dot{x}$.
Of course the velocity is proportional to the frequency - so an oscillator being driven at a higher frequency will lose more energy per cycle than an oscillator driven at a lower frequency.
On the other hand, the best coupling of energy into the system happens when the driving force is exactly 90 degrees out of phase with the amplitude (so force is in phase with the velocity) - which happens at the undamped resonant frequency.
As you increase the amount of damping, the "more energy lost per cycle" factor starts to beat the "more energy coupled in per cycle" factor. And that means that the effective resonance (largest response amplitude) shifts to lower frequencies.