There shouldn't be any problem with running CC on your tablet. It is a mystery to me why GP is complaining, because the Galaxy Tab 10.1 is officially listed as supported. Here is the list of supported Tab 10.1s.
Galaxy Tab 10.1(GT-P7500)
Galaxy Tab 10.1(SC-01D)
Galaxy Tab 10.1(SCH-I905)
Galaxy Tab 10.1(SHW-M300W)
Galaxy Tab 10.1(SHW-M380K)
Galaxy Tab 10.1(SHW-M380S)
Galaxy Tab 10.1(SHW-M380W)
Galaxy Tab 10.1v(p3)
Is the update an "official" one? If not, then there might be a problem with how the device is reporting itself to Google Play, for example as something other than a Tab. You can check what devices GP knows about by going to play.google.com, signing in, clicking on "My Orders & Settings" (at the bottom of the page), then the "Settings" tab. You should see all the devices that GP knows about. If the upgrade is official, is it new? It could be that GP needs some time to upgrade its devices database.
Another thing to try is to sign on to google play from your upgraded tab. It might help if you force GP to reinitialize itself. To do this, go to settings, apps, google play store and press "Clear Data", then restart GP. I don't know if this will change anything.
Unfortunately we have no control at all over how GP decides if a device is compatible. The only restriction we put on CC is that the device must be running Android 2.3 (Gingerbread) or higher. Clearly your tablet satisfies that restriction. Sigh...
EDIT: we also require that the device have WiFi. Is it possible that your tab doesn't have it?