The past form
The past form of should is used to express a mistake or missed opportunity. In this context, the past action did not happen, which leads to an attitude of regret or criticism. The past is formed by using should have + past participle.
I should have studied for the test (but I didn’t).
I didn’t study, and I regret it.
Amanda should have told me the event was cancelled.
Julie shouldn’t have told everyone her friend’s secret.
Julie told the secret, and the speaker is blaming her for it.
Asking a question
It is possible, although not very common, to ask a question using the past of should. In this case, the speaker is asking for advice about a missed opportunity or possible mistake.