Alfred
A custom search can be added to Alfred by clicking this link: alfredapp://customsearch/Fantastical/f/utf8/url=x-fantastical://parse?s={query}. Alfred must be installed for this link to work. More information about Custom Searches in Alfred can be found in Alfred's help.
LaunchBar
LaunchBar 5.1 supports native Fantastical integration. You can choose Fantastical in LaunchBar under LaunchBar's Preferences > Actions > Options.
Other Applications
Other applications can also use this URL handler to send sentences to Fantastical.
The syntax of the handler is: x-fantastical://parse?s=Sentence goes here