We just migrated to 10.1 this week (late to party, I know), but because of changes with Server and ArcObjects in the upgrade we can no longer use a couple of custom web services we used for our flow tracing capabilities with Network Analysis. In our case, I'll have to migrate it all to a Server Object Extension and publish it to our server, which is kind of a pain. In that case, esri.request would be how I'd interact with. http://resources.arcgis.com/en/help/main/10.1/index.html#/Server_object_extension_usage_in_client_ap...
Not sure how much help that is, but those are the routes I'm taking.
Note: Network analysis services cannot be used for performing utility network analysis on a geometric network. Instead, you'll need to use ArcGIS for Desktop. For more information, see What are geometric networks?
Does it mean that Utility Network Analysis can only be done in ArcGIS for Desktop?