There is definitely a sense of--both completion, and relief, as at the end of a long span of work, or the end of a beloved's illness, or the end of a prison sentence. Fulfilling the requirement and the commitment, and being finally free. That may be an odd thing to say about a show I have loved deeply and to distraction, but an ending, closure, a clear--if teary--eyed goodbye is better than being cut down by bad ratings or a pissy network exec who wants more T&A onscreen. Or 17 year old males instead of 37 and 40 year olds.
Rambling, sorry. The reality of ending won't finally hit until fall premiere season and there won't be a new SPN season. That will be the final nail, for me. But even with that, there are constant TNT reruns, Netflix rewatches, and glorious fic of fifteen years of fabulous writers, incredible art by amazing artists, and also incredible graphic art by photo manip magicians. And vids! This fandom taught me about vids, for which I'll be eternally grateful! The fandom arts are endless. And the charities spun by this fandom will go on, and keep the show's name forefront in people's minds for a long time. People with stories of time on the set, or random encounters with cast, or other meetings with people who made the show over all those years will continue to come forward. We haven't seen the "end" of Supernatural. All those reaction gifs? Those will still be relevant ten years from now...they will have passed into cliche, if they haven't already.
We saw Whoserface on Lucifer recently and I pulled up Jus im Bello and had DH watch it with me to meet "Nancy" as I first met her. He'd seen it, years ago, but his brain doesn't have retention for fandom and film stuff. So the Netflix archive is handy. And failing that, I have DVDs. Including the first Paley panel. It still ticks me off the second never made it onto a Season set of dvds--but at least we have the "Jensen doesn't think he's funny" segment on YouTube.
Tl;dr--I'm sad, in a way. But as the Major General said when the constables kept singing rather than going after the pirates, "Mabel, they *don't* go!" The Winchesters and friends are still around--wherever I look for them, they're there. It isn't goodbye, not really. Though I am glad their journey's done, and they ended up together and on their own terms.