I am a newbie tech worker in my first job at a small startup. I love it. Everyone has been very nice to me up until now, and I feel like I am very appreciated for bringing new ideas/solutions to the table.
Recently, I developed a proposal to improve a task that was previously carried out by other means; it was one of the loose-ends of the project. The proposal turned out to be a great success, more effective and faster as well. I got very excited and, after verifying the results, I emailed both my manager and the CEO about my new proposal. I am also working alongside the CEO in another parallel project, so it is not unusual for us to talk. I got happy replies from that email.
However, in today's meeting with my coworkers, the manager got quite upset at me and started the meeting by publicly blaming me of "skipping the hierarchy of the company" for involving the CEO in the email. I said I did not want to skip it, I included both because I felt it would be interesting for them to know. He added the CEO should not be bothered with every small detail because he has to take care of bureaucratic stuff as well, and we must only show the final product to him; furthermore, every decision must be communicated to him (my manager) before it is even heard by the CEO. I agreed with him, but also made it clear I did not know I was doing the wrong thing and blamed it in my lack of experience. He said "do not do it again" and proceeded to let someone else talk; I was the last one to talk in this meeting in this 3h meeting. To make things worse, in the little time I was left with, I pointed out a critical miscalculation in the current project which needs to be addressed immediately; I think this made him even more nervous but it is really a do-or-die thing...
I messed up for including the CEO in the list of recipients; I feel like I might have just been seeking positive feedback to be honest... However, I feel like the public rant was too much. I am just looking for advice, how should I address the current situation?