Hey Peter,
Sorry you lost this ability, Quick Edit is indeed quite convenient sometimes. I still have it working fine on my own installation of 3.8.1, so I’m curious about your site: what other plugins do you have installed? I see that you marked that you tried deactivating all these plugins – did you do that thoroughly? If so, did you notice any difference?
And just to be 100% clear: you’re talking about the “Quick Edit” functionality in the main Events list column in the admin, right? This is where you’re brought if you click the main “Events” link in the admin sidebar, with the calendar icon – it should lead to /edit.php?post_type=tribe_events in your admin.
— George