The Toffees bossed the first half at White Hart Lane on Sunday but were thwarted by Hugo Lloris on several occasions.
They then fell behind to a 65th-minute Emmanuel Adebayor strike, the Togo striker holding off Seamus Coleman before firing beyond Tim Howard.
The 1-0 defeat, which saw Spurs leapfrog Everton into fifth spot, was made even harder to swallow for Martinez as his side were denied what appeared to be a clear stoppage-time penalty after substitute Etienne Capoue clumsily took down Seamus Coleman.
"I haven't seen the replay but it looked a very sloppy incident," Martinez said afterwards.
"I think it was a careless challenge. He tries to win the ball and didn't at all.
"I'm not sure if there was enough contact for a penalty, but I've seen them given.
"You need a little bit of luck and it was one of those days for us."
Martinez was pleased with his side's first-half display as they took the game to Spurs.
"I think we started the game really, really well," the Everton boss said.
"My concern before the game was being able to come to White Hart Lane and be ourselves, control the game and impose ourselves on the opposition and we did that.
"It is fair to say at times in football you are better to be lucky than good and today we played the good role, not the lucky one.
"But I thought from our point of view the only criticism about the first-half performance is that you need to hit the back of the net with the chances we had.
"I thought Lloris was outstanding in two actions, but then we had three very, very good opportunities that on another day we would have scored that important first goal.
"In the second half, without reaching our real highs, I thought we restricted Spurs to very little.
"If you were to tell me Spurs would have one shot on target before the game, I would have taken that.
"Looking at the performance, it is disappointing because we didn't get the result but if we can take this performance into the next 13 games, we're going to get a lot of points. You hope football is not going to be that harsh on us again."