Dropped 3rd Strike - I blew it

[officialtony]

Help.
I can find nothing to help me out on whether I was wrong or right.
15-16 year olds. Fed Rules. 0 outs and 1-2 count. Low outside pitch and batter half swings. I am so focused on watching his swing. Convinced he went I spoke out and signalled with my right arm at same time - " he went, he's out ". Of course catcher drops ball. Everyone screams at batter to run and catcher to get ball. Catcher looks at me with the deer in the headlights look and throws wildly to 1st. F3 manages to hold onto ball but records no out. B1 is safe after throw.
Now it begins. Catcher says I called him out. His coach asks if I did. I said I did. We discuss this and after we are through, I leave the runner on 1st with no recorded out.
My question - was this the right thing to do?
The defensive coach was not the least bit irritated about my decision ( which scares me anyway ).
I did not call time, or dead ball or in any way prevent the ball from being live.
I know I blew the call. Should have been " he went, strike three ' and wait. What I am concerned about is what I did afterwards.
OK Fire away.

Thanks in advance.