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Modal + perfect infinitive (have + past participle) expresses judgments about the past: "should have" (a missed obligation), "could have" (an unrealized possibility), "might have" (uncertain past possibility), "needn't have" (unnecessary past action).
You should have call me.
You should have called me. — Use the past participle after "should have," not the base form.
You didn't need to bring a gift, but you did.
You needn't have brought a gift. — Use "needn't have" for an unnecessary action that was done anyway.
should have studied
might have forgotten