Hmm, unfortunately WordPress doesn't have Posts available by default to just drag into your editable menu. What you can do, however, is use the Links meta box and manually add the Post link. And instead of targeting a class that WordPress tacks onto menu items, that might also change and break your css in the future, you can check your screen options in the upper right of your Menus screen, and make sure you have "CSS Classes" checked in your Advanced Menu Settings.
This way, you can use your own class on that link you created and apply styles to that versus something that WordPress generates.
If you want to add a class dynamically, as in someone clicks this post link and WordPress knows that it's been clicked, and adds another class to the link, perhaps you can try a bit of JQuery - having an on Click event fire whenever that link has been clicked. Depending on how intelligent you need this link to be, you may be stepping into more advanced territory.
Hope the links help! Good luck!