The Merseyside club had more possession and chances than Tim Sherwood's side at White Hart Lane but were undone by Emmanuel Adebayor's strike in the 65th minute.
|5/1||Everton are 5/1 with Bet365 to win the FA Cup this season|
The loss leaves Everton two points behind Tottenham and five behind fourth-placed Liverpool with 13 Premier League games remaining.
"We dropped our concentration," Martinez said.
"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."
Despite failing to take at least a point from the fixture, Martinez believes similar performances will keep his side in the race for a top-four finish this season.
"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," said Martinez.
"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."