- I didn't see you at Sarah's party last night.
- I had to work yesterday, so I _____________ .
Do "couldn't go" (=had no possibility to do it) and "couldn't have gone" (= wouldn't have been able to do it) both work?
I'd be grateful if somebody could help me.
They're both correct. In most cases it wouldn't matter which you used.
However, "I couldn't go" is a simple consequence of having to work. "I couldn't have gone" says a little more. Being conditional, there is an implication of the condition, whether it is made explicit or not. In this case it could mean "I couldn't have gone even if I had known you expected to see me there; even though you missed me; even if I [had] wanted to ..."
But there's nothing in that two-line dialog that suggests whether the second speaker wants to say anything beyond the fact that s/he couldn't go because of work.