The Merseyside club had the better of much of the game at White Hart Lane but were unable to capitalise on their dominance with a goal.
Everton were made to pay for switching off in the second half, when Kyle Walker picked out Emmanuel Adebayor with a free-kick and the Togo striker fired in the winner with his left foot after bringing the ball down on his chest.
Victory for Tottenham moved them above Everton into fifth place and Martinez was left to rue the nature of Adebayor's winner.
The Spaniard said: "We dropped our concentration. When the free-kick was given for whatever reason we were feeling sorry for ourselves, because it could have been a free-kick going the other way just two seconds before.
"Nobody steps in front of the ball and, the backline, we don't recover quickly enough. Our backline is too spread out and that's our downfall."
Everton showed their attacking intent right from the off and Leon Osman had four opportunites to open the scoring in the first eight minutes.
Hugo Lloris produced one outstanding save to keep out the midfielder's left-footed strike and although the visitors continued to pose a bigger attacking threat, they were left empty-handed - much to the frustration of their manager.
Martinez added: "I think we started the game really well. My concern before the game was to be able to come to White Hart Lane and be ourselves, control the game and impose ourselves on the opposition and we did that.
"I think it's fair to say that sometimes in football you're better to be lucky than good and today we played a good role and we didn't play the lucky one.
"But I thought from our point of view the first half was a very good performance, if there's any criticism you need to hit the back of the net when you get the chances that we had.
"If you're going to tell me Spurs would have one shot on target before the game I would have taken that.
"Looking at the performance it's disappointing because you don't get a positive result, but if we can take this type of performance into the next 13 games we are going to get a lot of points."
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