Some applications stopped working properly after upgrading to OS X 10.9 Mavericks.
You need to enable access for assistive devices for the application.
In OS X 10.9 Mavericks the settings for enabling the access for assistive devices were moved from the Accessibility pane to the Security & Privacy pane.
To enable it for a specific application please open System Preferences ► Security & Privacy ► Privacy ► Accessibility
Now locate your application under "Allow the apps below to control your computer" list (the list is populated automatically by OS X) and click on the check-box next to it.
If the list does not contain Parallels Desktop, then drag and drop it manually from /Applications/ directory.