The Moyes loss against Wigan in 2013 was poor, 3-0 against Martinez's Wigan. Same year we lost 3rd round against Leeds in the League Cup. That year we didn't have Europa league and we totally could or should have won if the mentality was right.
What I'm saying is, if by February we're definitely not going to qualify for CL, and were obviously safe in the league, and we're in the 5th round of the cups or whatever, then we should consider resting players for the cup games...have key players miss a PL match or so (if it's not the Derby), and get the mentality of cups taking primacy right in the players's minds.
The CL teams play mostly kids and whatnot in the League Cup anyway, and outside of the usual suspects of United, Chelsea, arsenal and city there's no one really that should be beating us, and we have showed that we can fancy ourselves against them anyway on our day