Which phrase is correct and why? I think "something" is correct because we have a positive sentence not a negative nor a question. As i have seen from the internet (google search) the case with the "anything" is correct. Can anyone explain to me please why is that correct?
The case with anything is correct.
Your phrase is in fact negative, since "I was too surprised to ..." roughly equates to "Because of my surprise I did not...".
According to Meriam-Webster Dictionary:
something means an unspecified thing
anything means any thing whatever
Saying you were "too surprised to say something" technically means that there was a particular unspecified thing you did not say, when to be precise there were many possible things you might have said and you did not say any of them.
"I was too surprised to say anything" is more accurate, as not saying any thing whatever is equivalent to saying nothing at all.