> Do you think it's a correct reaction, also in terms of what I disclosed, or should I share the reasons why?

As far as work is concerned, the situation is far from critical. Disclose as much as you are comfortable to. But nothing is required or necessary. You are perfectly fine just apologizing and giving very evasive reasons "I'm tired / I was thinking about something else".

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I can see from comments people might think I advice you not to share the details. **It's not the case**. I believe only you can take such decisions, based on many factors that are completely personal. Read my answer as, right now, you're still free to do however you like, from a professional standpoint it's acceptable.