I would like
to have done something = I regret now that I didn't or couldn't do it:
- It's a shame we didn't see Anna when we were in London. I would like to have seen her again.
- We'd like to have gone away, but we were too busy at home.
You can use the same structure after
would love /
would hate /
would prefer:
- Poor David! I would hate to have been in his position.
- I'd love to have gone to the party, but it was impossible.