Seamus Coleman was tripped by Jan Vertonghen in the second half at Goodison Park but quickly bounced back to his feet and fired off a shot.
Martinez believes Coleman's eagerness to play on may have worked against him and can see why Kevin Friend did not point to the spot.
The Everton boss was also pleased that Friend had decided not to give Spurs a penalty in the first half after an incident between the same two players, in which he felt Vertonghen went down too easily.
"The first one is nothing. Vertonghen is trying to invite the challenge and use that contact to go down cheaply and easily," Martinez told Sky Sports.
"Unfortunately we have been punished a couple of times already this season with similar actions so I was pleased the referee did not point at anything.
"The second one, obviously Seamus didn't make a meal out of it but it looked like there was enough contact to stop him from probably getting a shot on target, so I felt that probably was a penalty.
"I can understand why the referee was quite happy to let it play after Seamus had reacted quickly."
Martinez was pleased to come through a tough test against Spurs and happy with how his side came back strongly in the second half after being under the cosh before the break.
"In the first half we found it a little bit hard to keep the ball, but we defended really well," he said.
"Spurs are a very good side and work extremely hard when they lose the ball. That probably upset our rhythm a little bit but then we found that rhythm in the second half.
"We imposed ourselves and created clear opportunities in terms of positions in the final third, and on another day we may have found that final pass."
Martinez also praised Tottenham goalkeeper Hugo Lloris for playing on after taking a knock to his head in a challenge with Romelu Lukaku.
The Everton boss insisted there was no malicious intent from Lukaku, who suffered a knee injury in the same collision which is not thought to be too serious.
"He picked up a knock but we hope it will not be a big problem and that he will be fine in the next 48 hours," said Martinez.