Shortcuts stopped working in Virtual Machines after OS X Mavericks upgrade. System shortcuts like CMD Tab are grabbed by OS X no matter what option is set for shortcuts in Parallels Desktop Preferences > Shortcuts.
Secure usage of Accessibility API in OS X Mavericks that requires user permission.
Allow Parallels Desktop to control your computer in System Preferences > Security & Privacy > Privacy > Accessibility
Click the lock and enter your administrator password to make changes.
Check on Parallels Desktop application: