Here’s a neat little online quiz to sort them out:
Generally speaking, I think it would be more common to hear “lost” used as an adjective than “missed” (but that doesn’t mean that “missed” isn’t also used as an adjective). For now, here are some of the various meanings — “miss” as a verb and “lost” as an adjective (for the above reason):
1. To fail to hit, reach, catch, meet, or otherwise make contact with.
2. To fail to perceive, understand, or experience: completely missed the point of the film.
3. To fail to accomplish, achieve, or attain (a goal).
4. To fail to attend or perform: never missed a day of work.
– a. To leave out; omit.
– b. To let go by; let slip: miss a chance.
6. To escape or avoid: narrowly missed crashing into the tree.
7. To feel the lack or loss of: Do you miss your family?
1. To fail to hit or otherwise make contact with something: fired the final shot and missed again.
– a. To be unsuccessful; fail.
– b. To misfire, as an internal-combustion engine.
The word lost also has a number of usages:
1. Unable to find one’s way: a lost child.
– a. No longer in the possession, care, or control of someone or something: a lost pen.
– b. No longer in existence; vanished or spent: lost youth.
– c. No longer known or practiced: a lost art.
– d. Beyond reach, communication, or influence: The expedition was lost to the world for two months.
3. Not used to one’s benefit or advantage: a lost opportunity.
4. Having not been or unlikely to be won; unsuccessful: a lost battle; a lost cause.
5. Beyond recovery or redemption; fallen or destroyed: a lost soul.
– a. Completely involved or absorbed; rapt: lost in thought.
– b. Bewildered or confused: I’m lost—can you start over?
I think you could say both “a lost opportunity” as well as “a missed opportunity” and the meanings would be basically the same. Unfortunately missed and lost are often not interchangeable at all.