I use AD as well and I make rock tracks, a genre where programmed drums will ALWAYS be apparent.
Your song actually sounds great, and programs like AD are perfect for those kind of genres where all you need is a beat.
As for humanizing the drum parts, here's some tips I've found useful:
Velocities matter! Here's what I like in AD:
Kick - 110-ish
Snare - 115-ish
Cymbals - 100 or below
Toms - 95 or so
Velocities are the biggest aspect of making drum parts sound human and AD especially starts to sound bad when every hit is maxed out.
I also send the tracks to individual ones in my DAW (Reaper) and mix it as if I recorded a real drummer. The FX that AD adds automatically really color the sound and kill you with volume. After all, presets are pretty much useless in the real world.
Here's a good article for you: 20 Tips On Creating Realistic Sequenced Drum Parts