Wigan appeared set to climb out of the relegation zone until Tom Huddlestone's free-kick was turned into his own goal by Emmerson Boyce in the final minute.
However, Martinez believes Jean Beausejour was fouled by Kyle Walker before the Tottenham full-back fell to the ground and that took the gloss of a performance which had left the Wigan manager proud.
"It should have been three points," Martinez told Sky Sports. "I thought the performance was magnificent from start to finish.
"Remember, we were playing against a side that are fighting to get into the Champions League spots, they've got tremendous quality and a wealth of talent in that squad.
"We gave them a goal, but even then we deservedly got in front and we feel hard done by the free-kick at the end. The referee got it wrong unfortunately and that has cost us two points.
"But, in terms of the performance, I couldn't be prouder. I thought tactically we showed incredible awareness and coped with anything that Spurs had to throw at us. To keep Spurs so quiet and the only threat was from dead-ball situations is full credit to the players."
Expanding on the award of the late free-kick, Martinez added: "It's very clear, you could see it live.
"Maybe the referee wasn't looking at the shoulder of Walker, but he has pulled Jean Beausejour on the shoulder and it should be clearly a free-kick for us.
"At that point we were too honest and tried to stay on our feet, and then Kyle gets a free-kick for his team. It's unfortunate for us, but with the experience of the referee he should have got that."