Table NRIV has no log changes activated in technical settings.
So that's no option.
I'm afraid that if you really want the number ranges back a restore from backup is the only option.
You could eventually recreate the number ranges but then you have to set all current numbers correctly...
That's more or less what Note 91212 - Number ranges overwritten by a transport also describes.
If you have a recent client copy of the affected client and not too much changed in the meantime, this could also help you to restore NRIV.
Because you refreshed the table via SE14 you did that at DB level as a drop table.
All clients are in the same DB table (client is a key field, all clients store there data in the same table...), so you also lost the number ranges of all other clients....
I would go for restore from backup.
Note that this is not an ABAP related question, "salvation" if it comes should come from database administration.
(Or are you able to identify and update each and every number range in your SAP system ?)
Try to identify the correct forum like http://scn.sap.com/community/oracle, http://scn.sap.com/community/db2-for-linux-unix-windows or any other DB forum in Forum Finder for the New SCN