As far as how to deal with the negative exposure you gave to the company and whether that was warranted or not, I guess everything has already been said in other comments/answers.
What I read between your lines, though, is that you might have also gone a bit too far into a defensive stance. You write:
I was called by the HR and she asked what made you tweet this. (1)
Apparently the CTO has copied the tweets and sent to her and two of my
supervisors. I told her it was miscommunication among my supervisors
and how I am the scapegoat when things go wrong for them. (2)
As to (1):
The way you put it, your HR department made an effort to understand what the issue was that made you tweet what you did. This is (was?) a chance for you to confront your company with what you felt would need improvement and for your company to act on it (you mentioned HR seeking "solutions").
As to (2):
This sounds like a total retreat on your part with blame going in all other directions but yourself in reaction to any confrontation. I agree with the other posters that you might have done something that you maybe should not have done and that the blame clearly lies with you.
Now you could argue that that was a very reasonable reaction to any circumstance that made you act the way you did, but if you refuse to explain what that circumstance is, then there is no way of settling this except for everyone walking away and realizing there is an unresolved dispute, is there?
Now in all of the above, I have no understanding of how different parts of your organization have communicated with you and what they gave you to understand. Depending on what type of blame they have put on you, that might of course change the picture slghtly.
Still, I personally believe, as with any other problem, if a boat is filling up with water, you should not resort to discussing who stole the buckets, but rather find and patch the hole.