Not that I'm happy with our recent Cup performances, but if big teams in the EPL struggle with squad size and rotation to stay competitive in European, League and 2 Cup competitions, then we really have no chance.
We play a style that generally works well over 38 games, but can be exploited in a one-off. Changing style just for Cup games is unlikely to work, so if we are to succeed in that area we might need to change our entire approach (and, I imagine would basically mean being more defensive). That is a high risk strategy given the potential downside of less league wins and still getting papped out the cups.
Striking the balance between league and Cups is never going to be easy given our financial constraints, but I'd rather see league success than Cup success in the long term.