You cannot retrieve a message you delete in Facebook, whether or not you sent it originally. However, the person who sent it and any people who received it still have access to the message if they have not deleted it. Facebook's "Archive" button can be confused with a delete button, so if you can't find a message in your Inbox, look in your Archive folder.
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Deleting Versus Archiving
Mousing or hovering over a conversation in the Messages panel and clicking the "X" that appears archives, rather than deletes, the conversation. To delete a single message in Facebook, open the conversation that contains it, click the "Actions" button above the message and click "Delete Message" or "Delete Messages" from the drop-down menu. If there is more than one message in the conversation, you must select the check box next to each message you want to delete and click "Delete." Select "Delete Conversation" from the Actions drop-down menu to delete all messages in a conversation.
Checking Your Archive
If you are not sure if you deleted or archived a message, check your Archive folder. On the Messages screen, above the list of conversations, click "More" and then click "Archived" from the drop-down menu.