If you look at the basic lift formula you'll see a few constants and a few bits that have a variable value. The V squared bit means that as you add a few more knots of airspeed, the C/L bit can bit reduced. Conversely, as you reduce airspeed, you'll still need as a much lift but the lift has to be supplied by the C/L element. Which means the air around the wind is having to work harder and the byproduct of that work is induced drag.
PM