Should' is the past tense of the word 'shall. ' When using the words 'should have' you are talking about something in the past that you 'ought to' or 'might have' done. Here are some examples: "I should have gone with you."

Is should not past tense?

English Grammar – Past tense of SHOULD – “I should have…”, “You shouldn't have..”, etc. The word 'should' doesn't follow the normal rules in English, when used in the past tense.

What tense should be used after should?

The simple past just tells what happened. Past modals tell what could have, would have, and should have happened. To form these past modals, use could, would, or should followed by have, followed by a past participle verb.