Everton missed the chance to put the pressure on fourth-placed Arsenal as they went down to Southampton at St Mary's.
The Goodison Park outfit were their own worst enemies as two goals from Antolin Alcaraz and Seamus Coleman gifted Southampton all three points.
Martinez conceded the timing of the first own goal from Alcaraz in the very first minute and Coleman's on the half-hour mark affected his side psychologically.
"It was a really difficult result to take," said Martinez. "The reality is to concede two own goals so early in the game made things nearly impossible.
"I did think that the second half we came out with a good attitude and good bravery but we needed that goal.
"When you want to win so much, and you concede two own goals, I felt psychologically we lost a bit of confidence and our normal arrogance in our play."
Martinez also felt luck wasn't on his side as he felt they should have won a penalty in the second half when Leon Osman went down in the box under a challenge from Dejan Lovren, with the Everton midfielder being booked for an apparent dive.
"We needed that goal," Martinez continued. "We had a couple of chances for Lukaku in the second half and for me it was a penalty on Leon Osman.
"There were key moments when we needed that little bit of luck. It could have been a different ending if we had got that goal."