Lynn,

The spots are not the work of the viburnum leaf beetle. The good news is Viburnum carlessii is not one of the favorites of this beetle. It is one of the most resistant species.

Your shrubs have the symptoms of some type of leaf spot disease. It is not possible to identify the exact disease from a photo.  The following link will take you to a website that discusses leaf diseases. By closely examining your shrub and comparing the symptoms to the photos on the site you may be able to narrow down the possibilities. The site also discusses management strategies.

http://www.extension.umn.edu/garden/yard-garden/trees-shrubs/management-of-leaf-spot-diseases/

Just in case you have other species of viburnums, I am including a link to the Cornell website that provides excellent information about the beetle.

http://www.hort.cornell.edu/vlb/index.html

I hope this information is helpful. Please reply back if you have additional questions. Thank you for using our system.