I've always thought that is such a weird way of judging success. The only competitions that really matter if you win (as an English team) are the Premier League and Champs league, with the FA Cup a distant 3rd. The League Cup isn't too much more relevant than the International Champions Cup they play over in the States in the off-season.

And as for the posterity argument, I guarantee more people will remember this Liverpool side - even if they win nothing - than the United side winning Europa or some other big team winning the FA Cup