Well, it's pretty easy to hide things from people on FB, so unless they are technology-challenged you could posit that they had a valid reason.
Mention it to them and ask why you weren't invited. Don't get confrontational, you can do it kiddingly, maybe with some mock sarcasm, whatever works best for your personality.
If they didn't have a good reason and they do it again it is time to evaluate your relationship with them; it may be a way of them saying buzz off without them having to actually tell you.
I'm with Carl on this one, both of the options you mentioned are at the ends of the spectrum, you should try and walk the midway, find out why they didn't ask you to come, maybe it slipped their mind or maybe they had guests they thought you and the Mrs. wouldn't be comfortable with.
I think you should have them killed.
JED, you've really been at it with the sarcastic answers lately. Hahah.
What hasn't been mentioned. Perhaps the BBQ invitations were limited to folks with a commonality that predates your relationship with the hosts. One example would be a group who initially met as part of a social or business group a few years before the couple hosting the BBQ met you.
Another thing to remember. "One robin does not a Spring make." there could be any number of simple, logical explanations, including an erroneous belief that you'd be out of town than day, or otherwise simply not able to attend. Then there's always simple thoughtlessness on the part of the hosts.
Your post is a bit ambivalent. Are the friends mentioned the hosts or was it the entire group? People often do have separate social circles. A small example would be your friends from work and your friends from church...the groups could quite easily overlap or equally easy be mutually exclusive.
^ This. People are allowed to have parties and invite who they want to. It doesn't mean that you were being purposefully excluded, just that they had a group that was particularly included.
That's one of the perils of Facebook, though. You see what other people are doing when sometimes that doesn't include you. And that can be hard, and it can be tempting to jump to conclusions. I have done so myself at times.
Plus I have friends on Facebook from different parts of my life. And when you have a party with people from different groups, some of which don't know each other, as a host you have to spend a significant amount of party time making sure some of those people feel welcome (which can be a challenge when there's more food to put out and ice buckets to fill and lots of people who you haven't had a chance to catch up with yet).
Sometimes the better route is separate parties, or going out for happy hour or whatever.
If you can get away with the ask/kidding route that Carl suggested, that might work. That way you find out why and get it out in the open (albeit at the risk of looking whiny or petulant; I don't know you or your friends, so I can't say).
Or try and take the high road. Just have a get-together at your place and invite them. I'm not saying pretend it didn't happen, but try not to take it personally. If they behave as it nothing's wrong, there wasn't.
I wouldn't give it too much thought.
You say "a few friends had met up" for the barbecue, but who was the host? The friends you're connected to or some other group? As others have pointed out, the BBQ group may have some connection you're not part of or there may have been limitations of space; it may have been for a specific occasion like someone's birthday or some other milestone for a person you don't know.
Myself, I wouldn't ask about it and make things awkward.
Lots of people around here lately that seem to want to abandon friendships, relationships, etc. over the most insignificant slights. You aren't owed an invitation to everything. Maybe they forgot. Maybe they thought you were busy. Maybe they needed a smaller guest list for some reason, and you didn't make the cut. Maybe they were throwing the barbeque because of something that had nothing to do with you. Maybe they thought they invited you, and wonder why you no-showed.
Whatever ... its just a barbecue. You weren't entitled to an invitation.
You don't have to pretend it didn't happen. You just ought to react to it like a grown man that didn't get invited to a BBQ ... not a teenage girl that didn't get invited to a birthday party. Next time you're around them ... tell them the barbecue looked fun. See what they say. Then move on with your life.
Or, go in with guns blazing, explain why you were entitled to notification, tell them off ... and don't get invited to the next one either. Life's too short to get offended at little crap like this. Unless you have enough friends that you can spare these ... I wouldn't fight over it.