The easiest way is, disappointingly, only available in Steam's Big Picture mode. The filtering, there, is more enhanced, and can work as an answer to your previous question, in addition to this one.
If you activate Big Picture mode (click the game controller at the top-right), then you can go into Library, then click Games, and click Filter Games, on the right side of the page. With this, you can setup more complex filtering than you can in the normal client. Personally, I hope they add these features into the normal client, soon.
You can see an example, from mine, here.
Since there's no real way to search for the absence of a tag, you'd have to select all of the tags that you want, and leave out that tag. If there's a more convenient way to do this, from within Steam, I'm unaware of it, yet.