There is a growing number of fans who are becoming increasingly disgruntled with the Toffees boss after another season of underachievement.
Everton are 14th in the Barclays Premier League table having won just four matches at home all term and, despite an FA Cup semi-final to look forward to, having also reached the last four of the Capital One Cup, the natives are becoming restless.
There were 'Martinez Out' banners at the weekend's match at Watford and there are likely to be more protests during Wednesday's game at Crystal Palace but the Spaniard is adamant he is not feeling the heat.
"As a manager, you understand that there is always the pressure you put on yourself," he said.
"With the scrutiny of the outside or not, you always follow an intense way of working which, in the last seven years I have been involved in the Premier League, has always been the same, and I won't stop doing that.
"You need to be very consistent as a manager; you need to be able to work under the demands this position requires, and I wouldn't say that is any different to what I have done in the last seven seasons at this level.
"You cannot control outside scrutiny. As a manager you concentrate on what you can affect, and we can affect many things from now until the end of the season."
Footage has emerged of Martinez involved in a discussion with a supporter at Monday night's under-21s victory over Chelsea at Southport, although it is only a video and nothing of the conversation can be heard.
The Toffees boss said he welcomes dialogue with fans, although he dismissed any suggestion the exchange was anything other than friendly.
"It is not a confrontation. I always want to know what the fans feel, and I always respect a fan who supports our club who has a genuine interest in the club," he added.
"I have enormous respect for people who share passion for the club - Evertonians have been through a lot but now is my third season here and I understand and share their frustrations.
"We will never look away from a fan's opinion - if I have an opportunity to share a few moments with a fan, I will always do that as it is important to know how fans feel.
"I have no problems with the passion the fans have towards the team and the club, because that is the strength we have as a club and we will do everything we can to make them proud.
"I can understand the frustration. I can understand that in our football club we all share an incredible amount of passion.
"We are as disappointed as the fans are. We need to be close together to use each other's strength.
"The only thing that matters to us is to make sure we finish the season really strong and get high up the table."
Martinez admits Everton have been their own worst enemies this season, losing a number of matches they should have won.
"There is not such a thing as blame," he said.
"We put a lot of work into assembling this squad which breeds excitement and incredible potential but the reality is we have been really good in certain aspects and really poor in others.
"We have thrown really good positions away. Clearly we need to get better.
"We are in a significant moment of the season. There is no time to look back but just be as good as we can in the next game."
Everton will be without captain Phil Jagielka for the next two matches with a hamstring injury but the defender has not yet been ruled out of their Wembley semi-final on April 23.
"I think it is too early to make that assessment," Martinez said
"Phil is always a quick healer and we will have a better idea on Monday or Tuesday next week."