I agree with you on managers not prioritising the cups, something I can never grasp. No it is not Ashleys fault entirely for this. However Rafa is not the first and wont be the last manager to play the kids in these cups, if you are the manager of Chelsea or Man U your squad is usually a little thicker with better players on the peripherals, clubs like Newcastle have a starting 11 and maybe a couple of good players sitting on the bench, but our squad depth is shyte (please no one say "its Shite") as is most of us lower Premier league clubs. So when you are in a relegation battle, as a Manager do you want to risk your stars getting over tiered (something I also disagree with) or injured, playing Bury on a cold December in a early round league cup game? As a fan I do, but Managers don't.
So with a little investment if we were not annual relegation fodder, our Manager might just risk a cup game. So that is where I put some blame onto Ashley, Ultimately though it's the Manager who picks the team.