I SHOULD HAVE asked about the tickets. I think it's too late now.
You NEEDN'T HAVE worried about giving the presentation. You were really good!
He MUST HAVE done really well in the interview for them to offer him the job so quickly.
I couldn't find my keys and I thought I MIGHT HAVE lost them in the park.
They COULD HAVE joined us in Vietnam, but they decided to stay longer in Laos.
past possibility
criticism of past actions
certainty about the past
lack of necessity or obligation in the past
past possibility