A 1-1 draw with Southampton means the Toffees have taken just 17 points out of a possible 51 at Goodison Park this season and are now guaranteed to finish with their lowest home points tally in top-flight history.
The atmosphere at Goodison Park has been worsening by the week and there is an increasing number of supporters who blame Martinez for their underachievement.
One took it upon himself to invade the pitch late in the game and confront stand-in captain Leon Osman before directing a volley of a abuse at Martinez, stood in his technical area, and being led away.
"We all understand that the results at home have not been anywhere near what we expect," said Martinez, who in the week was filmed having a discussion with a supporter while watching the under-21s in Southport.
"We have been talking a lot about the contrasting seasons we are having away from home and at home and it is understandable you get that frustration.
"But we have a really good opportunity to take advantage of where we are.
"We are competing in the (FA Cup) semi-final and we have games where we want to make fans proud.
"That is what we are going to do from now until the end of the season, make sure they are proud of our performances and results."
Ramiro Funes Mori's 68th-minute goal was cancelled out eight minutes later by Sadio Mane's close-range strike but there was more bad news for Everton with Seamus Coleman limping off.
With a Merseyside derby at Anfield on Wednesday and Manchester United awaiting at Wembley on Saturday the last thing Martinez needed was more defensive injuries with Phil Jagielka and Leighton Baines both missing this game.
"He felt his hamstring and we will assess him in the morning but it will be hard to see him being involved this week as that sort of injury takes longer than a week," added the Toffees boss.
Southampton dominated the game and were unlucky to leave with just a point after hitting the woodwork three times.
"I am disappointed about the final result," said boss Ronald Koeman.
"Of course if you are 1-0 down in the second half and you get a point out of it that is positive but it is not what we wanted to have.
"It was not sharp enough in the team performance
I was disappointed after 45 minutes that we didn't create more and didn't score a goal.
"It was not good enough in the final pass and there were not enough shots on target.
"It is a big opportunity we lost today to win the game."
Source : PA
Source: PA