A similar thing happened to me recently on another airline with a downgrade from J to Y. After several attempts at contacting customer services by phone and email I finally got a pathetic apology with a promise of a partial refund within a few days but I’m still waiting 5 weeks later.
I’m getting tempted to put a comment on their facebook wall and joining twitter just so I can put a public tweet on their page too as that seems to help slightly.
Failing that, if you paid with a credit card you could apply to dispute the charge (as you didn’t get what you paid for) or write to their legal department setting out your claim for a breach of contract.
Emirates do have a refunds claim form on thier website where you can claim for a refund for downgrades but I assume you have tried that?