This is the kind of stupid thing that makes Liverpool fans sound so bitter and excuse making, Hodgson has never had success because he's not won a useless cup?
Different teams have different expectations, its as simple as that, 10th in the league is incredibly successful for one team and a dismal failure for another one, if you can't comprehend that no one can really help you. Hodgson has IIRC beaten Liverpool in 2 out of 3 games, home and away, despite spending what, 1/3rd of the wage budget, maybe 1/10th the transfer budget, that is what is called success.
Liverpool just spent 100mil, on top of an already expensive team(don't give me net spend rubbish, Liverpool are one of the most expensively RUN teams in the country, they should be doing significantly better than West Brom), a league cup isn't a very good return, better than a kick in the nuts, doesn't make up for not being top 6 or pushing for higher.
EDIT:- Are liverpool getting Euro football from the cup win whatever happens in the league? If so, I wouldn't expect a dramatic improvement, theres going to be a bunch of extra games to play, for basically the same squad, maybe a couple more players.