If your domain expired and was deleted from your myCP, technically it is no longer your domain. It was dropped and became available for anyone to register as a new name. Unfortunately you cannot file a domain dispute, which is used only when domains have been fraudulently transferred to another registrar. As you did not own the domain any longer, this action is not appropriate.
You can contact the current registrant to see if they are interested in selling the domain to you. Many times they have purchased the domain but perhaps they do not have any plans for using it. To look up the current whois information of a domain, you will want to visit sites such as http://whois.domaintools.com/
It is important to understand, once a domain expires and drops into the available pool of domains, anyone can register the domain as a new name. You are no longer the current registrant, and unless there is a trademark involved, you may not have any rights to the domain even if you were the previous registrant.