Wait---are you sure? If the pinion turns the wrong direction, it will not spin up into the flywheel. Did you put on the pinion upside down? No, you can't because there is a flange on the bottom. Same thing if you wound on the rope in the wrong direction: Pinion will not rise into the flywheel.
Well, I'm puzzled.
Attach some photos and please give the year of the engine.