Are phrases with implicit meanings considered incorrect/wrong?

An example phrase is

... Internet is out ...

The implicit word here is "connection." The full phrase would be

... Internet connection is out ...

Is the first incorrect? Is there a general rule to acceptance of dropped/implicit words in phrase meaning?

The general rule is "If your readers (or hearers) will understand it without the word, you can omit it. If they are going to be confused or misled without it, don't".

Out of context "internet is out" may not have that meaning: when I first read your question I read it as a fashion statement, like "The internet is no longer cool" or something. (I'm not being funny, I really did). But in context, it is fine.

it's okay, you were merely being elliptical

Characterized by extreme economy of expression or omission of superfluous elements.