Seamus Coleman, who conceded a penalty in the 2-0 victory over Aston Villa last Saturday, appeared to be fouled by Jan Vertonghen in the 65th minute of the clash at Goodison Park, but the Irishman recovered his footing to see his deflected effort go wide.
Referee Kevin Friend waved away the hosts' appeals for a spot-kick and Martinez believes Coleman's honesty potentially denied his side a golden opportunity to break the deadlock.
"I think Seamus gets impeded, the only thing is that he doesn't overreact, he doesn't look for the penalty," the Everton boss said.
"He just gets back on his feet. And that allowed the referee not to have to make a decision.
"He was clearly impeded and it should have been a penalty."
Both sides knew victory would lift them into second in the Premier League after 10 matches, but it was the visitors who started much the brighter.
Martinez conceded that his players were slow out of the blocks, but he was delighted with Everton's much-improved showing after the break.
"It was two different halves from our point of view," the Spaniard added.
"In the first half we lost the ball too quickly. It becomes a difficult game. I was pleased when we managed to defend throughout that period, with good intensity and good focus.
"Second half was completely different. I thought we imposed ourselves better, we kept the ball for longer spells and we were the ones forcing Spurs to defend.
"You saw two teams that weren't happy with the draw, two teams driving forward to try to get the winning goal, which is always refreshing."
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