In the end this sums it up best. I have always tried to avoid knee jerk reactions in all walks of life, particularly football. He had a fantastic season last season, which to me earns him the right to have a disappointing one this year. This also has to go alongside an acknowledgement that whatever manager we employed after Moyes was going to need time to put their own style and philosophy on a club that had had a manager for well over a decade. During that transformation it may have been a rocky road.
I have to say I have always admired both Everton fans and Everton as a club, as one that doesn't buck to modern trends. Football is now a huge commercial business and with the growth of social media has allowed fans to access the club and discuss things in a way that there haven't been in previous decades. This does however lead to a short termism, a "knee jerking" for want of a better word.
Having said that, having given Moyes the job and the job description of rebuilding the team it was an outrageous decision to sack him (note I said having given him the job) the same is true with Martinez. I would hate us to go sacking someone before they were given enough time to make it work. The way Chelsea conduct themselves to me is the opposite of how we should look to behave. At the heart of Everton is and should be a fairness.
Not only is it ethically sound, but it's the most efficient way of doing things. The costs involved in replacing a management team would not bode well for us. Also clubs who have continually changed managers have underperformed, it breeds an instability. In particular Spurs who have had a lot of managers haven't delivered much on their extravagant spending.
I remember at various times under Moyes when we had a difficult patch, there were those who wanted us to sack him to bring in the latest flavour of the month. Sometimes it was Coyle, sometimes Paul Jewell. I don't think either of those managers would have been as good as Moyes.
So yes, by all means people should be critical of Martinez. This season is not going well. But short of looking like we are going to get relegated I am not sure getting rod of him serves much purpose. By September next year, I will hope he has started to build a team in his own image though.