The "not equal to" option is not available for the product tag condition. I am guessing @Kine was using the product type condition instead of product tag. You could change the product type of the items you want to hide to something unique ("Wholesale", "Hidden", "Special", etc), and then use the "not equal to" condition on the product type.
NOTE: you will have to use the "all conditions" match type on your smart collection for this to work properly. There is no way to make this work using the "any conditions" match type when using more than one condition on your collection.
Thanks! I set up a new product type and am able to exclude it from the All Products and All Collections results, but now I'm having other problems hiding it from site search. I'm reading through dozens of posts on the forum about hiding from search results, but nothing seems to work. I've already set the seo metafield tag as suggested, but the item still shows up in site search.
Are you using the default Shopify search? That seems to contradict the Shopify docs if you have correctly set the seo metafield. If Shopify is not behaving according to their own docs, then you might have to take it up with Shopify support. Nobody on the forum can help with that!
In the meantime, you really only have two options: