I don't think you're getting what I'm trying to say here. 9-1 defeat, is a one off. We can all put setbacks down to bad luck etc...
Let's instead take the record home defeats as an example. I'd guess that Martinez is aware of that. Furthermore, I'd propose his professional pride is hurt too. Because of the longevity, an entire season. Not just a one-off. And because it's being used as a stick to beat him with.
It may be to late to rectify it but, I could be wrong here, it wouldn't surprise me to see Everton's cavalier approach tempered. After all, look at the Chelsea game and to a certain extent our defensive performances in the new year compared to last. To me, he looks like he is attempting to find a suitable balance to between attack and defense.
Can it be improved, yes and to a degree I think his defenders have let him down. But I see improvement, change, adaptability. I don't think we should be so quick to judge him after the Arsenal result. Let's see what transpires until the end of the season.