True to form, I have/had the same problem. I removed our antenna after we moved into the house 6 years ago. It, too, rust-stained the shingles.
Thing is, if you clean off the rust, you'll want to clean the ENTIRE roof. Otherwise, your roof will be clean in just the area in question. I wouldn't use a power washer on the problem. A garden hose and a cleaning solution should be all you need.
I, unfortunately, don't know of anything that can clean the rust off of the shingles. (This doesn't mean a solution doesn't exist.) Either consult a Roofer or a Roofing Supply House (found in the Yellow Pages under ROOFING SUPPLIES), or go to a job site and ask the guys doing the work. They're all your best sources for info. As for my house, well, the rust is still up there! It's kinda 'grown' on me as part of my home's original character. In about 10 years, I'll need new shingles anyways. After a while, you won't even notice it.
My best to ya and hope this helps.
PS: Be sure you get the PROPER cleaning instructions on using whatever 'solution' you use. It may be hazardous to your grass and/or plants if it runs down and out the gutter. And wear gloves. Be safe up there too!