At first I had the same problem, but after installing the unity-webapp-* packages I managed to install gmail, gplus, facebook, calendar and youtube. The only issue is that the counter doesn't work on the icons.
For example, the gmail icon on unity left panel doen't display the counter of new messages. The same happens with facebook and google plus (in this case I receive at least a notification of new posts). When I tried webapps in ubuntu 12.04 that worked at least for gmail.
At first I had the same problem, but after installing the unity-webapp-* packages I managed to install gmail, gplus, facebook, calendar and youtube. The only issue is that the counter doesn't work on the icons.
For example, the gmail icon on unity left panel doen't display the counter of new messages. The same happens with facebook and google plus (in this case I receive at least a notification of new posts). When I tried webapps in ubuntu 12.04 that worked at least for gmail.