By the end of January, they'll have played thirteen games in two months (ten PL, three League Cup) that will have necessitated using a very strong squad. Not exactly desirable when you're a couple results from safety.
Perhaps if we had played our best team, we may have been in with a chance of a cup and European qualification, but no good worrying about that now, Sunderland got and deserved a win, that will do heaps for their morale, nice to have "knocked out by the eventual Cup winners" on our history, and they would not be the first team to win a cup and get relegated!