Getting DPM Alerts for Failed Recovery Point for Database that has Been Deleted
DPM is checking the consistency of the SharePoint meta-base, which is not consistent anymore due to you deleting the database in SQL Server. That is, you have removed the logical/physical database in SQL Server but you have not removed references to it from the SharePoint metadata. My advice to you is to restore the database that you deleted and then remove it correctly via the SharePoint PowerShell cmdlets.

There is a really good article on removing orphaned databases here:

http://social.technet.microsoft.com/wiki/contents/articles/30558.sharepoint-2013-deleting-orphaned-sharepoint-databases.aspx

And a list of all database-related cmdlets can be found here:

https://technet.microsoft.com/en-us/library/ee906544.aspx