No Applications after Backup recovery

I used to backup my data via Airport Time Capsule and configured my backup, so that no Applications are part of the backup. In case of a broken HDD etc. I would prefer to install only those applications I really need and not all the other legacy crap which comes with the time...

Now the time has come and I've got a "new" (late 2012) Macbook Pro. I powered it on and set it up just as usual. After the first boot I opened the Migration Assistent in order to recover my backup from the time capsule. Somehow nothing happened after entering the APT credentials for my Account, so I tried it with the CMD+R mode during the boot process.

This worked just fine. I entered my credentials and the recovery process began. After completion the MBP restarted and I had a normal desktop with all my files. My backup recovered.

Unfortunately now there is no "Applications" directory in my User dir. There are also no applications like "Safari.app" or even "System Preferences.app". When I try to change the Desktop Background (which I thought would open the System Preferences) nothing happens. All Dock-Items are represented by an "?" - except Finder which seems to be the only app which is still there.

I booted the system via CMD+S in order to search for those applications. find . -name "Safari.app" had no results. As a proof that find works I searched for a file I know that exists in my backup: find . -name "certain_file.jpg" and I had a correct result. I don't even have a terminal (except the CMD+S shell).

The MBP was shipped with OS X Yosemite and apparently the system recovered without any Applications.

What now? How can I get at least all my standard applications?