... But you can use TSP. PLEASE read the container BEFORE you leave the store. You'll need gloves and goggels, among other things, when you go to use this stuff.
I wouldn't use a power-washer. It will easily force water behind the shingles. Forget about those little asphalt 'tabs' that are installed between each shingle and the one next to it. They're meant to keep rain from getting behind the shingles; not water under pressure.
Wet the surface then scrub on the diluted TSP. Rinse with a spray stream from the hose. Start from the bottom up; NOT the top down. (If you start from the top, you'll get 'clean streaks', and they'll stand out very noticibly.) My best to ya and hope this helps.