Social Media can be a real nightmare. When you only share your best moments, people can think you are bragging, or being "fake". But when you open up too much and share your feelings, what you write is open to all kinds of misinterpretation.
I'm not a social media guru, in fact I hate it and rarely make posts. My general approach to it is by all means share real thoughts and feelings, but don't publicly "cry" about stuff. It is instantly interpreted as attention seeking, and the general response "U OK Hun?" has become something of a joke.
But this isn't social media advice - what's done is done, and you want to fix things.
Let me just address your concerns:
"To say that what was in the post was untrue would be a lie."
True, but that doesn't mean you should have said it. You can't "unsay" it, but this is social media and you can delete it. I'd suggest doing so, if you haven't already. This doesn't mean it wasn't true, and it doesn't delete it from your friend's memory, but it does send a message that you regret saying it at least, and that is something. Most adults know that we all think stuff but don't say it, and we all cope with the knowledge that our friends probably do say stuff behind our backs that we should never hear about because frankly therein madness lies.
"To say that I should not have felt that way, and only did because of work pressure, doesn’t really constitute an apology."
Agreed. And for the reasons I gave in my last point, it is okay to feel things. It only became a (possible) problem because you said it.
"To apologise for making the post would imply that I felt fully justified in being upset by his success, and the only mistake I made was not keeping quiet about it."
Firstly, you may not need to apologise for offending him at all. But I'll get to that, as well as what you may want to say. But even if you do apologise for the post, there is no implication of the sort. Regret is regret, and if you regretted saying it, that ought to be enough. More useful is why you felt the way you did, not why you posted, and again I'll get to that.
"To emphasize that I was grateful for the invite would likely sound like I was sarcastically emphasizing the differences between us."
Depending on how you say it, this may not be the case. Saying you appreciated the invitation is a nice thing, unless of course you add or imply "but I didn't actually enjoy it". I don't think you need to do that, however. If you re-think the whole episode and get to the root of why you feel the way you do then you may be able to look back at the event and appreciate it properly.
Here's why you may not need to apologise - you only said you friend's demeanour has changed, and that he seems offended. I'm assuming he did read your post but you appear to be assuming the offence. There are other things he may be feeling - guilt perhaps?
If he really is your friend then he wont want to deliberately make you feel rubbish. Okay, so some people do brag and rub their brilliant lives in other's faces, but I don't think you'd be so worried about retaining the friendship of someone who was inherently like that. Plus, you say he's "successful" because he has a nice house and a family. Those are quite normal, achievable things. It's not like you said he has a speedboat and a holiday home in Monaco. It seems to me that the real reason you feel some jealousy is because you haven't got those perfectly reasonable things, not because he is disgustingly rich and rubs it in your face. I have to say, I think you are in the wrong, and if he's your friend he may feel sorry for you right now, he possibly feels some guilt over the way his offer of hospitality and friendship made you feel, and he may also be distant because he doesn't know how to discuss the matter with you.
I would say approach him, and perhaps say:
I really appreciated your invitation the other night. If I've seemed a bit down since, it isn't your fault. I hoped I would have a family by now, and I can get a bit down about it when I'm around people who have all that.
Don't assume he's offended. Remember it may be other things he is feeling.
Don't mention the house. I know that was one of the things you were jealous of, but keep the material stuff out of it. That does make you look bad. But a family is an admirable goal, and is partially out of your control if you're choosy, which you should be. Plus, if you have a family then getting a big house is easier because there are two of you, plus all the breaks you get for having children.
And lastly don't assume he has seen, or mention the SoMe post (which hopefully you have deleted by now). If you mention it, then it was definitely meant to be seen by him.
See how he responds. If he has a beef, he'll raise it now. If he was offended by the post, then by all means go on to say:
I didn't mean to offend you. Really, it's not about you or what you have, it's about what I don't have. I'm sorry about the post, I wasn't thinking, I just let my negative feelings get the better of me.
I think this addresses the post, apologises, but doesn't attempt to go back on anything you said so stays true to your feelings.