Thanks to @JanHudec for reminding me that the graph is for a level flight.
To keep the flight level at low speeds, the Angle of Attack(AoA) needs to be increased, meaning Cl (coefficient of lift) must be increased and so the lift-induced drag ( proportional to Cl^2) is high at low speeds.
With the increase of speed, AoA decreases to keep the flight level, hence, Cl and so lift-induced drag and its Thrust Required (Tr) decreases.
Coming to Zero-lift Drag or the parasitic drag. At low speeds it is low. But at higher speeds, there is an introduction of wave drags,
"parasitic drag increases because the fluid is striking the object with greater force, and is moving across the object's surfaces at higher speed. As speed continues to increase into the transonic and supersonic regimes, wave drag grows in importance."-Wikipedia.
Therefore, in the case of Zero-lift, the increase of velocity is not much of the reason (by this I mean, not the proportionality with the square of velocity), but the increase of wave drag is. And so there is not much effect on Induced drag with the increase of velocity