«Стыдно» means you did something incorrectly and you regret it.
I believe embarrassment doesn't imply you've done something wrong, so I think «неудо́бно» or «нело́вко» would work better for describing embarassment: «Мне бы́ло о́чень неудо́бно/нело́вко».
Or you could use the participle «смущённый»/«смущённая»: «Я была́ о́чень смущена́» (masculine «Я был о́чень смущён»; short forms sound better here), which is grammatically closer to the English counterpart.
I think embarrassed works in a simple case such as Мне стыдно. It can be embarrassed or ashamed, but being "ashamed" in English is stronger than стыдно in Russian. Embarrassed is more on the same level as "мне стыдно," unless the person has done something VERY shameful in his own eyes, in which case he would be "ashamed." Неудобно is uncomfortable and works in the same sense in English. Неловко is awkward, and this direct translation works directly in the same way in English. Стыд can be shame or embarrassment, dependent on the gravity of how "стыдно" the person feels. It's just an opinion, not an absolute argument on my part.
When someone feels a certain way, in Russian, it feels that way "to oneself."
Мне стыдно. Тебе холодно. Ему/Ей жарко. Нам весело. Вам грустно. Им спокойно.
"To me is embarrassing," is how "I'm embarrassed," is constructed in Russian. Same thing with
"To you it is cold," meaning, "You're cold."
To him/her it's hot = He/she is hot.
To us it's fun = We're in a fun mood.
To you (plural) it feels sad = You (plural) are sad.
To them it's calm = They're calm.
In Russian, we just say those sentences have no subject.
In English, a sentence requires a subject. When a sentence has no subject, we use a dummy pronoun ‘it’ that doesn’t refer to anything in particular:
- It is cold. = Холодно. — ‘it’ doesn’t refer to anything mentioned before, it’s just a way to refer to some unnamed envioronment.
Sometimes, ‘it’ refers to something mentioned before:
- When I touch the mirror, I feel it’s cold. — Когда я трогаю зеркало, я чувствую, что оно холодное. — it refers back to ‘mirror’, so we actually use it in the Russian translation.
So, the English ‘it’ has two distinct functions:
- when it refers to environment or situation in general, it’s a dummy ‘it’ and we don’t use it in the translation,
- when it refers to something mentioned before, we translate it with «оно», «он» or «она» (depending on the gender of the thing mentioned).
Yes, I thought you were replying to @szeraja_zhaba's comment because you wrote "in this case." His second example of зеркало being оно.
Then to answer your question, in the case of this exercise, "мне было стыдно," the verb is было in the sense of "It was embarrassing to me." Again, with the "it" in English meaning what it was that embarrassed me.