Modals about the past

A modal plus have plus the participle judges the past. Must have is a firm deduction, can't have its opposite: she must have left, he can't have seen us. Might have and could have are possibilities.

Should have is a criticism or a regret: you should have told me. Needn't have says something was done for nothing: you needn't have brought food, while didn't need to may mean it was not done.

In speech, have shrinks to a sound like of, so write it carefully: must have, could've, never must of.