He's working under utterly awful conditions, much, much worse than Moyes ever has.
I think Whelan has basically budgeted for a wage bill of 35 million (which in Pl terms is peanuts, only reading less than pay that) and Martinez has to fund any wages above that by selling players.
Basically Martinez has to sell a good player for big money every year and replace him with someone cheaper to afford the wages he needs to buy and keep players good enough to keep them up. This year they'll go down simply because everyone else has increased their wages and bought in better players and wigan haven't been allowed to. This'll be their first year since Jewell where they're paying one of the three lowest wages in the league and Jewell was allowed to pay transfer fees without selling his best players first.
Under those conditions most managers would take them down.
The problem with this, from everton's point of view, is there's basically two ways to finacially overachieve. One is in the market, you buy players who are better than their clubs value them as and sell them for mroe than their worth. Martinez is, largely he has bought some stinkers, very good at that. But, his players tend to be overpaid. Their agents get them deals which make them the 15th best paid squad in the country and martinez gets performances out of them that leave then 16th. If his players aren't as good as martinez and their agents think they are, then you'd have to suggest that martinez isn't improving those players by coaching or tactics. Moyes was, our team was according to wages the tenth best in the league and finished 6th.
But, having said that, he'd be working with better players at everton so possibly his tactics would be much more effective with defenders who can actually defend.