It's a fair enough point in theory I'm just not sure why you're so confident this is likely to change. Didn't Martinez get dumped out of a bunch of prior Cups to lower league opposition? I'm not even so much arguing the idea of league v. Cups as I am the idea that certain managers are better in Cups. He had a good run last year but why is that "the real Martinez" v. his pretty lousy record prior to this year?
2011/2012
F.A. Cup 3rd Round Swindon Town 2 - 1 Wigan Ath.
League Cup 2nd Round Crystal Palace 2 - 1 Wigan Ath.
2010/2011
F.A. Cup 4th Round Replay Wigan Ath. 0 - 1 Bolton Wdrs.
League Cup Quarter Final Arsenal 2 - 0 Wigan Ath.
2009/2010
F.A. Cup 4th Round Replay Wigan Ath. 0 - 2 Notts. County
League Cup 2nd Round Blackpool 4 - 1 Wigan Ath.
A lot of those teams have less/equal money to Wigan so the money excuse doesn't wash (aside from Arsenal loss of course).
Those early exits to lower league opposition didn't mean he couldn't win a Cup; however the Cup win doesn't mean the lower league losses can't happen again. For any team outside the top 4/5 Cup performance looks fairly random.