Learn Italian: Saremmo rimasti per il tramonto, è il nostro rimpianto. - We would have stayed for the sunset, it is our regret.

The verb rimanere (to stay) is a verb of state or being. Just like in the passato prossimo, verbs of motion and state take essere as their helping verb instead of avere. To form the past conditional, we use the present conditional of essere (saremmo) plus the past participle.

Why does the past participle end in "-i" (rimasti) instead of "-o"?

Whenever a compound tense uses essere as its helping verb, the past participle must agree with the subject in gender and number. Since the subject is a plural "we", the ending changes to the masculine plural rimasti. If "we" referred to a group of only women, it would be rimaste.

The English translation says "it is our regret", but where is the word for "it"?

In Italian, you do not usually need a subject pronoun for "it" before the verb essere (to be). The verb è on its own perfectly translates to "it is" in this context without needing a filler word.

How does the word rimpianto tie into the grammar of this sentence?

Rimpianto means a regret. The past conditional (saremmo rimasti) is the perfect tense to pair with this noun because it expresses an unfulfilled desire or missed opportunity in the past: something you would have done, but did not actually do.