Everton are 11th in the Premier League and their hopes of winning a trophy ended when they lost their FA Cup semi-final to Manchester United. Martinez said he appreciated why his future at Everton was being questioned.
"I understand it completely because I never felt that being Everton manager is a manager to be judged by being in an average position," he told a news conference on Thursday.
"I always encourage huge expectations. As a football club we have to drive to challenge for silverware and the top four, and when you aren't there the scrutiny needs to be there," he said.
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"The signs are there but we aren't the finished article. I'm more capable now to find the final adjustments to make us better."
Asked about reports that Everton supporters were planning to protest during Saturday's Premier League clash with Bournemouth, Martinez called for unity.
"The message (to the fans) is we are all hurting together. I understand their passion and as a football club they make us what we are. Football without passion makes no sense.
"But... only when you get through those difficult experiences and those painful moments do you get a renewed drive to fight more than ever and find a way of challenging for silverware."
Martinez confirmed that the injured trio of Phil Jagielka, Seamus Coleman and Gareth Barry would miss the visit of 14th-placed Bournemouth, along with suspended defender Ramiro Funes Mori.
(Reporting by Simon Jennings in Bengaluru; Editing by Mark Heinrich)
