Everton went into the weekend in seventh place, knowing that a win at Selhurst Park could have taken them as high as third in the Premier League.
Despite generally controlling the game and recording five more shots on goal than their hosts, the Merseysiders were unable to make the breakthrough and had to settle for a draw - a result that gave Palace just their fourth point of the season.
And manager Martinez believes a bluntness in forward areas cost his side the chance to win.
"We couldn't find that little bit of sharpness in the final third," the Spaniard said.
"Overall, we probably allowed ourselves to get a bit frustrated. Every time the ball went out of play it took ages to come back in.
"It was a stop-start sort of game and we couldn't get in a position to break them down.
"They were very well organised, worked extremely hard and made it very difficult."
Although Martinez was disappointed with his own side's attacking display, he had words of praise for the hosts' gritty performance.
"The whole backline played really well, had good intensity, they put their head where it hurts and picked up a really important clean sheet. You have to give credit where it is deserved.
"We will always be critical of ourselves and you'll always look for ways to break a solid team down, but I've seen it many times that you can play a game like today and get caught on the counter. I am very pleased that we did not allow that to happen."