Learn English – Can you “regret” someone else’s action

Remorse is deeper and stronger than regret. One sense of regret is

A feeling of sadness, repentance, or disappointment over something that has happened or been done.

You may have associated regret with Italian "rimorso" because a deed was done. But regret is not limited to the above sense; it can also be used to talk about deeds that weren't done, ie also has sense

A feeling of sadness, repentance, or disappointment over something that hasn't happened or hasn't been done.

Regret thus seems to correspond with your "rimpianto" in that, in your example, you focus on the deleterious consequences of an action (or inaction).

As well, regret may be used of acts (of commission or omission) performed by others.

Remorse addresses the speaker's moral sense of personal guilt. It is directed inward, a gnawing feeling of distress over one's own responsibility for one's own grave error—in many cases a sense of having sinned; while regret is directed outward—an unmoralized feeling of distress over the unhappy consequences of an act which may have been performed (or omitted) by anyone.

So remorse can be your rimorso if, in your example, you are using the same sense of "doing something wrong."

As John Lawler notes:

They're both fine, they mean the same thing, and the only reason to use a perfect gerund construction (having told) instead of a normal gerund (telling) is to emphasize the remote pastness of the event, which is now regretted, instead of making it unclear how much time had passed between the deed and the regret. There are situations (like a death) which make that relevant, and therefore justify the extra construction and parsing costs. Otherwise, a normal gerund will do the job.