FA Cup this season would feel like a consolation prize, granted, because the league was there for the taking this year and we've cocked it up royally.
What is a "major" trophy is not quantifiable but the reaction to the FA Cup was partly relief about winning a trophy after so long and partly a recognition of the FA Cup's history and status.
No-one would have been reacting like that over a league Cup win. No-one would have supported Wenger signing a new contract on the back of it.

Why are you inventing stuff?
Really? You're doing the "you know you are, you said you are" thing again? Sheesh.