But, at sub-zero Selhurst Park on Saturday, his Everton side finally showed signs of a thaw and perhaps even the odd green shoot of recovery.
The Spaniard and his squad arrived in south London having won only once in their previous 13 games, a run that began in November.
At that stage, they were just four points off fourth place and Martinez looked like he may be set to steer his side back to the promised land of the Champions League.
But things quickly soured at Goodison Park and, before Saturday, only four points separated Everton from the relegation zone. Questions, meanwhile, have been asked of Martinez’s future.
A trip to Palace, four wins out of four in the honeymoon period following Alan Pardew’s appointment as manager on January 2, looked like exactly what Everton did not need.
But, within two minutes, one ugly touch from Romelu Lukaku, who bundled home Steven Naismith’s low cross with his chest, was enough to secure the visitors their first win since December 15.
Martinez said: “You do not only learn a lot about your players during runs like these, you learn about the football club.
“About the people around the staff, our fans — they have been incredible. From the outside when you get bad results people are quick to criticise or highlight whatever they want to highlight.
“But our fans have been incredibly supportive. Look at today. Look at the way that they’ve been travelling in big numbers. That has made me aware that we’ve got a very special football club where we can learn a lot.
It has been a bizarre and completely unexpected two months for Everton and their manager, who earned so many plaudits after leading his side to the top five last season, his first in charge at Goodison Park.
But this was a timely victory with next weekend’s Merseyside derby looming.
“I think you learn as a manager to concentrate on the things that you can affect,” he added. “Obviously if I’d started believing in all the things I read last I’d have been too big-headed even to speak to my wife.
“I’ve been very fortunate to have been involved in football now with clubs that allow me to work.
“You are going to get difficult periods and good periods but you can’t lose sight of what you have to do tomorrow to affect the next game. I think we’ve had that.”
And what of Pardew, whose bright start in charge has now been dimmed? “No, same attitude, same application,” he said, when asked whether a new approach would be taken following his first defeat in charge.
“We will hopefully defend the first two minutes better than we did today and we can get ourselves a better result.”
CRYSTAL PALACE: Speroni, Ward, Dann, Delaney, Kelly (Zaha 65), Puncheon, McArthur, Ledley, Gayle, Chamakh (Mutch 25), Sanogo (Murray 71).
Subs Not Used: Mariappa, Hangeland, Campbell, Hennessey.
EVERTON: Robles, Coleman, Stones, Jagielka, Baines, Besic, Barry, McGeady, Naismith, Mirallas (Oviedo 68), Lukaku (Kone 90).
Subs Not Used: Gibson, Distin, Barkley, Alcaraz, Griffiths.
Ref: Roger East (Wiltshire).