This is because as speed decreases, it requires less power to produce a given amount of thrust. The following is a thrust-speed curve for a 1 watt engine:
The engine is operating at a constant propulsive efficiency ($η$) of 1 - this means that the shaft-power (RPM × Torque) gets converted into thrust-power (thrust × speed) with 100% efficiency¹. We can see that at 1 m/s, we obtain 1 newton of thrust from the 1 watt engine. The important thing to remember is that thrust is inversely proportional to speed.
If the aircraft slows down from the minimum thrust speed, it would certainly need a greater amount of thrust to oppose the drag. However, since the speed has reduced, the power required to produce that thrust has also reduced. As a result, the minimum power speed is slightly less than the minimum thrust speed - at this speed, the power required (thrust × speed) is minimum, even though thrust alone is not.
¹of course in practice, $η$ is not constant - it itself varies with speed, but the reasoning for why the minimum power speed is less than the minimum thrust speed remains the same.