Quite certain clubs charge considerably less for the cup comps (unless Europe). I know I've managed to get tickets reasonably easily for those games. As an example, I know, and have bought, £10 tickets for arsenal league cup games which included man city. I'd be surprised if the premier league clubs were charging more than £25.
Edit, I've just checked spurs' site and general sale was £25 for adults, St holders was £20 and family tickets ranged between 40-50 (2 adults and 2 juniors)