Arsene Wenger's side scored towards the end of each half, through Olivier Giroud and Tomas Rosicky, to seal the points and leave Everton with one win from their last 11 league matches.
Martinez, however, was encouraged by his team's performance, and feels a positive result is all they are missing.
"I thought we controlled the game well, I thought we defended Arsenal very well," he told BT Sport.
"The disappointment is to concede a goal from a dead-ball situation [Giroud's goal having come from a corner]. That is something that you can affect a bit better.
"The scoreline does not reflect what happened on the pitch, and that is positive.
"That could be, from our point of view in terms of individual performances and the way that we performed in the second half, the story of our season in the league, and we need to change that.
"In football you play for results and unfortunately, at the moment, we are not getting what we deserve."
Everton have slipped to 14th position in the Premier League, just six points from the drop zone.
Martinez accepts his side are in a relegation battle, but insists that is true of any club yet to reach the 40-point mark.
The Spaniard added: "It is always a relegation scrap for any team until you get to 40 points, that is the nature of our league.
"We just want to win games consistently and create momentum.
"Today the performance did not give us a reward in the result, and that is something that has happened too many times this season."
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