Fresh from completing the scoring in Thursday night's impressive 2-0 UEFA Europa League win at Wolfsburg, Kevin Mirallas gave Everton the lead after 15 minutes with a spectacular long-range strike.
Christian Eriksen brought Tottenham level before Roberto Soldado's strike in the first minute of first-half injury time handed Martinez's men a first defeat in nine matches across all competitions.
"We're really disappointed because I don't think the players deserved to finish with that empty feeling at the end," he told reporters.
"We started the game really brightly, we scored a magnificent goal, which is the hardest thing in football - scoring that first goal away from home.
"I did feel at that point we could have just killed the game and gone for the second goal but we couldn't really find that rhythm. Then the game went into a little bit of a strange moment where Spurs ended up hitting the back of the net twice in a fortunate manner.
"You'd then think that Spurs were going to come out, dictate things and take the game away from us, but it wasn't the case.
"We reacted extremely well, we had to be expansive, we had to put in a lot of effort, and I thought the performance in the second half put us in good positions, and we should have taken advantage.
"But, overall, I'm pleased with the performance, because it's not an easy place to come and the energy levels that we showed, the commitment, even some phases of our football were really, really good. It's a tough scoreline to take when I didn't think our performance deserved that."
Martinez was unhappy with referee Michael Oliver's decision not to give an 89th-minute penalty when Romelu Lukaku's header struck Federico Fazio's arm, but insisted the responsibility for the defeat lay ultimately with his players.
"I'll never blame a decision like that for not getting a result, it happens, it's part of the game," he added.
"But I'm disappointed because Michael Oliver is a really good referee and when the ball contacted the arm he wasn't in an obstructed view and I think it should have been spotted. It was a real shame.
"I would never blame a third party for us not getting a result, though. We should be good enough to come to White Hart Lane and get a result."
