I wish I could offer legal but I can only offer support by being here to listen.
I am not asking for details but i assume this was reported to them by some "official".
In my opinion, if we look at the bigger picture; given recent events in football, they just see an adult and a minor, a sexual offence (as you was convicted) and are protecting the image of the F.A. against accusations by others who have a louder voice than you.
I am not saying just accept their actions but just be open to the consequences of a highly emotional stand against them. Calmly look at your options in a cold and calculated manner. Think of what further damage could be given to you and not just hope to revitalise a dream to play at a higher level.
Depending on your football skills and aspirations; what would be the reasons for highlighting the incident again to the media. The F.A. can afford better lawyers than you and costs could be high, you have been convicted so not much is going for you, sorry.
Personally I would concentrate on the other qualities, skills and experiences you have to redefine your future life; try to image you have stopped playing for another reason so change these emotional negative aspects to a positive perception for your future.
It's your decision but there will always be individuals here to listen and support as part of their dream to stop any one re-offending or against injustice.
Learn from yesterday, live for today, hope is for tomorrow else what is left if you remove a mans hope.